diff --git a/toolchain/check/convert.cpp b/toolchain/check/convert.cpp
index 985440093e22..e942c6b97296 100644
--- a/toolchain/check/convert.cpp
+++ b/toolchain/check/convert.cpp
@@ -954,16 +954,47 @@ struct InheritanceEdge {
 // derived to base.
 using InheritancePath = llvm::SmallVector<InheritanceEdge>;
 
+// Try to complete the type if it's a class type or contains a class type. This
+// allows us to look up information about base and adapt relationships which are
+// defined in the class body.
+static auto TryToCompleteClassType(Context& context, SemIR::TypeId type_id,
+                                   SemIR::LocId loc_id) -> bool {
+  // We want to complete the type if it _is_ a class, or there's a class type
+  // somewhere inside it, such as a tuple with a class.
+  //
+  // TODO: For now, we use a heuristic to find types that may contain a class
+  // type. This matches the types that we recurse into in
+  // TypeCompleter::AddNestedIncompleteTypes.
+  //
+  // FacetType is intentionally omitted from this list. We do not recurse into
+  // facet types looking for class types in TypeCompleter.
+  if (!(context.types().Is<SemIR::ArrayType>(type_id) ||
+        context.types().Is<SemIR::StructType>(type_id) ||
+        context.types().Is<SemIR::TupleType>(type_id) ||
+        context.types().Is<SemIR::ClassType>(type_id) ||
+        context.types().Is<SemIR::ConstType>(type_id) ||
+        context.types().Is<SemIR::CustomLayoutType>(type_id) ||
+        context.types().Is<SemIR::MaybeUnformedType>(type_id) ||
+        context.types().Is<SemIR::PartialType>(type_id))) {
+    return true;
+  }
+  return TryToCompleteType(context, type_id, loc_id);
+}
+
 // Computes the inheritance path from class `derived_id` to class `base_id`.
 // Returns nullopt if `derived_id` is not a class derived from `base_id`.
 static auto ComputeInheritancePath(Context& context, SemIR::LocId loc_id,
                                    SemIR::TypeId derived_id,
                                    SemIR::TypeId base_id)
     -> std::optional<InheritancePath> {
+  if (!context.types().Is<SemIR::ClassType>(derived_id)) {
+    // Don't try to complete non-class types.
+    return std::nullopt;
+  }
   // We intend for NRVO to be applied to `result`. All `return` statements in
   // this function should `return result;`.
   std::optional<InheritancePath> result(std::in_place);
-  if (!TryToCompleteType(context, derived_id, loc_id)) {
+  if (!TryToCompleteClassType(context, derived_id, loc_id)) {
     // TODO: Should we give an error here? If we don't, and there is an
     // inheritance path when the class is defined, we may have a coherence
     // problem.
@@ -1473,8 +1504,8 @@ static auto PerformBuiltinConversion(Context& context, SemIR::LocId loc_id,
           context.types().GetTypeIdForTypeInstId(src_pointer_type->pointee_id);
       // Try to complete the pointee types so that we can walk through adapters
       // to their adapted types.
-      TryToCompleteType(context, target_pointee_id, loc_id);
-      TryToCompleteType(context, src_pointee_id, loc_id);
+      TryToCompleteClassType(context, target_pointee_id, loc_id);
+      TryToCompleteClassType(context, src_pointee_id, loc_id);
       auto [unqual_target_pointee_type_id, target_quals] =
           sem_ir.types().GetTransitiveUnqualifiedAdaptedType(target_pointee_id);
       auto [unqual_src_pointee_type_id, src_quals] =
@@ -2009,7 +2040,11 @@ auto Convert(Context& context, SemIR::LocId loc_id, SemIR::InstId expr_id,
   // TODO: Is there a risk of coherence problems if the source type is
   // incomplete, but a conversion would have been possible or would have behaved
   // differently if it were complete?
-  TryToCompleteType(context, context.insts().Get(expr_id).type_id(), loc_id);
+  // TODO: We should not need to do this unless we're looking for a base or
+  // adapt. But lower crashes without it, so we must be failing to complete a
+  // type somewhere else when it is required.
+  TryToCompleteClassType(context, context.insts().Get(expr_id).type_id(),
+                         loc_id);
 
   // Check whether any builtin conversion applies.
   expr_id = PerformBuiltinConversion(context, loc_id, expr_id, target);
diff --git a/toolchain/check/testdata/facet/convert_class_type_to_generic_facet_value.carbon b/toolchain/check/testdata/facet/convert_class_type_to_generic_facet_value.carbon
index d00afd2f1f8c..4d1bcc6f90f1 100644
--- a/toolchain/check/testdata/facet/convert_class_type_to_generic_facet_value.carbon
+++ b/toolchain/check/testdata/facet/convert_class_type_to_generic_facet_value.carbon
@@ -74,11 +74,11 @@ fn G() {
 // CHECK:STDOUT:   %empty_tuple.type: type = tuple_type () [concrete]
 // CHECK:STDOUT:   %Generic.generic: %Generic.type.30d = struct_value () [concrete]
 // CHECK:STDOUT:   %Generic.type.ee14e9.1: type = facet_type <@Generic, @Generic(%Scalar)> [symbolic]
-// CHECK:STDOUT:   %Self.8ea1ea.1: %Generic.type.ee14e9.1 = symbolic_binding Self, 1 [symbolic]
-// CHECK:STDOUT:   %Generic.WithSelf.F.type.390775.1: type = fn_type @Generic.WithSelf.F, @Generic.WithSelf(%Scalar, %Self.8ea1ea.1) [symbolic]
-// CHECK:STDOUT:   %Generic.WithSelf.F.b85a66.1: %Generic.WithSelf.F.type.390775.1 = struct_value () [symbolic]
-// CHECK:STDOUT:   %Generic.assoc_type.d7021d.1: type = assoc_entity_type @Generic, @Generic(%Scalar) [symbolic]
-// CHECK:STDOUT:   %assoc0.31052a.1: %Generic.assoc_type.d7021d.1 = assoc_entity element0, @Generic.WithSelf.%Generic.WithSelf.F.decl [symbolic]
+// CHECK:STDOUT:   %Self.8ea: %Generic.type.ee14e9.1 = symbolic_binding Self, 1 [symbolic]
+// CHECK:STDOUT:   %Generic.WithSelf.F.type.390: type = fn_type @Generic.WithSelf.F, @Generic.WithSelf(%Scalar, %Self.8ea) [symbolic]
+// CHECK:STDOUT:   %Generic.WithSelf.F.b85: %Generic.WithSelf.F.type.390 = struct_value () [symbolic]
+// CHECK:STDOUT:   %Generic.assoc_type.d70: type = assoc_entity_type @Generic, @Generic(%Scalar) [symbolic]
+// CHECK:STDOUT:   %assoc0.310: %Generic.assoc_type.d70 = assoc_entity element0, @Generic.WithSelf.%Generic.WithSelf.F.decl [symbolic]
 // CHECK:STDOUT:   %GenericParam: type = class_type @GenericParam [concrete]
 // CHECK:STDOUT:   %empty_struct_type: type = struct_type {} [concrete]
 // CHECK:STDOUT:   %complete_type: <witness> = complete_type_witness %empty_struct_type [concrete]
@@ -87,7 +87,7 @@ fn G() {
 // CHECK:STDOUT:   %.e53: <witness> = impl_self_witness %ImplsGeneric, @Generic, @Generic(%GenericParam) [concrete]
 // CHECK:STDOUT:   %Generic.impl_witness: <witness> = impl_witness @ImplsGeneric.as.Generic.impl.%Generic.impl_witness_table [concrete]
 // CHECK:STDOUT:   %Self.685: %Generic.type.b40 = symbolic_binding Self, 1 [symbolic]
-// CHECK:STDOUT:   %Generic.WithSelf.F.type.e39: type = fn_type @Generic.WithSelf.F, @Generic.WithSelf(%GenericParam, %Self.8ea1ea.1) [symbolic]
+// CHECK:STDOUT:   %Generic.WithSelf.F.type.e39: type = fn_type @Generic.WithSelf.F, @Generic.WithSelf(%GenericParam, %Self.8ea) [symbolic]
 // CHECK:STDOUT:   %Generic.WithSelf.F.d19: %Generic.WithSelf.F.type.e39 = struct_value () [symbolic]
 // CHECK:STDOUT:   %Generic.assoc_type.c13: type = assoc_entity_type @Generic, @Generic(%GenericParam) [concrete]
 // CHECK:STDOUT:   %assoc0.b4a: %Generic.assoc_type.c13 = assoc_entity element0, @Generic.WithSelf.%Generic.WithSelf.F.decl [concrete]
@@ -113,11 +113,6 @@ fn G() {
 // CHECK:STDOUT:   %U.af9edd.2: %Generic.type.ee14e9.2 = symbolic_binding U, 1 [symbolic]
 // CHECK:STDOUT:   %PassThroughToGenericMethod.type: type = fn_type @PassThroughToGenericMethod [concrete]
 // CHECK:STDOUT:   %PassThroughToGenericMethod: %PassThroughToGenericMethod.type = struct_value () [concrete]
-// CHECK:STDOUT:   %Self.8ea1ea.2: %Generic.type.ee14e9.2 = symbolic_binding Self, 1 [symbolic]
-// CHECK:STDOUT:   %Generic.WithSelf.F.type.390775.2: type = fn_type @Generic.WithSelf.F, @Generic.WithSelf(%T, %Self.8ea1ea.1) [symbolic]
-// CHECK:STDOUT:   %Generic.WithSelf.F.b85a66.2: %Generic.WithSelf.F.type.390775.2 = struct_value () [symbolic]
-// CHECK:STDOUT:   %Generic.assoc_type.d7021d.2: type = assoc_entity_type @Generic, @Generic(%T) [symbolic]
-// CHECK:STDOUT:   %assoc0.31052a.2: %Generic.assoc_type.d7021d.2 = assoc_entity element0, @Generic.WithSelf.%Generic.WithSelf.F.decl [symbolic]
 // CHECK:STDOUT:   %CallGenericMethod.specific_fn.151: <specific function> = specific_function %CallGenericMethod, @CallGenericMethod(%T, %U.af9edd.2) [symbolic]
 // CHECK:STDOUT:   %H.type: type = fn_type @H [concrete]
 // CHECK:STDOUT:   %H: %H.type = struct_value () [concrete]
@@ -206,15 +201,15 @@ fn G() {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !definition:
 // CHECK:STDOUT:   %Generic.type: type = facet_type <@Generic, @Generic(%Scalar.loc4_25.1)> [symbolic = %Generic.type (constants.%Generic.type.ee14e9.1)]
-// CHECK:STDOUT:   %Self.loc4_33.2: @Generic.%Generic.type (%Generic.type.ee14e9.1) = symbolic_binding Self, 1 [symbolic = %Self.loc4_33.2 (constants.%Self.8ea1ea.1)]
+// CHECK:STDOUT:   %Self.loc4_33.2: @Generic.%Generic.type (%Generic.type.ee14e9.1) = symbolic_binding Self, 1 [symbolic = %Self.loc4_33.2 (constants.%Self.8ea)]
 // CHECK:STDOUT:
 // CHECK:STDOUT:   interface {
-// CHECK:STDOUT:     %Self.loc4_33.1: @Generic.%Generic.type (%Generic.type.ee14e9.1) = symbolic_binding Self, 1 [symbolic = %Self.loc4_33.2 (constants.%Self.8ea1ea.1)]
+// CHECK:STDOUT:     %Self.loc4_33.1: @Generic.%Generic.type (%Generic.type.ee14e9.1) = symbolic_binding Self, 1 [symbolic = %Self.loc4_33.2 (constants.%Self.8ea)]
 // CHECK:STDOUT:     %Generic.WithSelf.decl = interface_with_self_decl @Generic [concrete]
 // CHECK:STDOUT:
 // CHECK:STDOUT:   !with Self:
-// CHECK:STDOUT:     %Generic.WithSelf.F.decl: @Generic.WithSelf.%Generic.WithSelf.F.type (%Generic.WithSelf.F.type.390775.1) = fn_decl @Generic.WithSelf.F [symbolic = @Generic.WithSelf.%Generic.WithSelf.F (constants.%Generic.WithSelf.F.b85a66.1)] {} {}
-// CHECK:STDOUT:     %assoc0.loc5_9.1: @Generic.WithSelf.%Generic.assoc_type (%Generic.assoc_type.d7021d.1) = assoc_entity element0, %Generic.WithSelf.F.decl [symbolic = %assoc0.loc5_9.2 (constants.%assoc0.31052a.1)]
+// CHECK:STDOUT:     %Generic.WithSelf.F.decl: @Generic.WithSelf.%Generic.WithSelf.F.type (%Generic.WithSelf.F.type.390) = fn_decl @Generic.WithSelf.F [symbolic = @Generic.WithSelf.%Generic.WithSelf.F (constants.%Generic.WithSelf.F.b85)] {} {}
+// CHECK:STDOUT:     %assoc0.loc5_9.1: @Generic.WithSelf.%Generic.assoc_type (%Generic.assoc_type.d70) = assoc_entity element0, %Generic.WithSelf.F.decl [symbolic = %assoc0.loc5_9.2 (constants.%assoc0.310)]
 // CHECK:STDOUT:
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = %Self.loc4_33.1
@@ -328,9 +323,9 @@ fn G() {
 // CHECK:STDOUT:   %Scalar.loc4_25.1 => constants.%Scalar
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific @Generic.WithSelf(constants.%Scalar, constants.%Self.8ea1ea.1) {}
+// CHECK:STDOUT: specific @Generic.WithSelf(constants.%Scalar, constants.%Self.8ea) {}
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific @Generic.WithSelf.F(constants.%Scalar, constants.%Self.8ea1ea.1) {}
+// CHECK:STDOUT: specific @Generic.WithSelf.F(constants.%Scalar, constants.%Self.8ea) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: specific @Generic(constants.%GenericParam) {
 // CHECK:STDOUT:   %Scalar.patt.loc4_25.2 => constants.%Scalar.patt
@@ -341,11 +336,11 @@ fn G() {
 // CHECK:STDOUT:   %Self.loc4_33.2 => constants.%Self.685
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific @Generic.WithSelf(constants.%GenericParam, constants.%Self.8ea1ea.1) {
+// CHECK:STDOUT: specific @Generic.WithSelf(constants.%GenericParam, constants.%Self.8ea) {
 // CHECK:STDOUT: !definition:
 // CHECK:STDOUT:   %Scalar => constants.%GenericParam
 // CHECK:STDOUT:   %Generic.type => constants.%Generic.type.b40
-// CHECK:STDOUT:   %Self => constants.%Self.8ea1ea.1
+// CHECK:STDOUT:   %Self => constants.%Self.8ea
 // CHECK:STDOUT:   %Generic.WithSelf.F.type => constants.%Generic.WithSelf.F.type.e39
 // CHECK:STDOUT:   %Generic.WithSelf.F => constants.%Generic.WithSelf.F.d19
 // CHECK:STDOUT:   %Generic.assoc_type => constants.%Generic.assoc_type.c13
@@ -368,10 +363,6 @@ fn G() {
 // CHECK:STDOUT: specific @Generic(constants.%T) {
 // CHECK:STDOUT:   %Scalar.patt.loc4_25.2 => constants.%Scalar.patt
 // CHECK:STDOUT:   %Scalar.loc4_25.1 => constants.%T
-// CHECK:STDOUT:
-// CHECK:STDOUT: !definition:
-// CHECK:STDOUT:   %Generic.type => constants.%Generic.type.ee14e9.2
-// CHECK:STDOUT:   %Self.loc4_33.2 => constants.%Self.8ea1ea.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: specific @CallGenericMethod(constants.%T, constants.%U.af9edd.1) {
@@ -403,17 +394,6 @@ fn G() {
 // CHECK:STDOUT:   %U.loc21_57.1 => constants.%U.af9edd.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific @Generic.WithSelf(constants.%T, constants.%Self.8ea1ea.1) {
-// CHECK:STDOUT: !definition:
-// CHECK:STDOUT:   %Scalar => constants.%T
-// CHECK:STDOUT:   %Generic.type => constants.%Generic.type.ee14e9.2
-// CHECK:STDOUT:   %Self => constants.%Self.8ea1ea.1
-// CHECK:STDOUT:   %Generic.WithSelf.F.type => constants.%Generic.WithSelf.F.type.390775.2
-// CHECK:STDOUT:   %Generic.WithSelf.F => constants.%Generic.WithSelf.F.b85a66.2
-// CHECK:STDOUT:   %Generic.assoc_type => constants.%Generic.assoc_type.d7021d.2
-// CHECK:STDOUT:   %assoc0.loc5_9.2 => constants.%assoc0.31052a.2
-// CHECK:STDOUT: }
-// CHECK:STDOUT:
 // CHECK:STDOUT: specific @CallGenericMethod(constants.%T, constants.%U.af9edd.2) {
 // CHECK:STDOUT:   %T.patt.loc15_31.2 => constants.%T.patt
 // CHECK:STDOUT:   %T.loc15_31.1 => constants.%T
diff --git a/toolchain/check/testdata/facet/convert_class_value_to_generic_facet_value_value.carbon b/toolchain/check/testdata/facet/convert_class_value_to_generic_facet_value_value.carbon
index 8d7757e7f76a..8cdeb498d1b5 100644
--- a/toolchain/check/testdata/facet/convert_class_value_to_generic_facet_value_value.carbon
+++ b/toolchain/check/testdata/facet/convert_class_value_to_generic_facet_value_value.carbon
@@ -134,11 +134,6 @@ fn B() {
 // CHECK:STDOUT:   %pattern_type.4e0: type = pattern_type %Generic.type.ee14e9.2 [symbolic]
 // CHECK:STDOUT:   %U.patt.8a6: %pattern_type.4e0 = symbolic_binding_pattern U, 1 [symbolic]
 // CHECK:STDOUT:   %U: %Generic.type.ee14e9.2 = symbolic_binding U, 1 [symbolic]
-// CHECK:STDOUT:   %Self.8ea1ea.2: %Generic.type.ee14e9.2 = symbolic_binding Self, 1 [symbolic]
-// CHECK:STDOUT:   %Generic.WithSelf.F.type.390775.2: type = fn_type @Generic.WithSelf.F, @Generic.WithSelf(%T, %Self.8ea1ea.1) [symbolic]
-// CHECK:STDOUT:   %Generic.WithSelf.F.b85a66.2: %Generic.WithSelf.F.type.390775.2 = struct_value () [symbolic]
-// CHECK:STDOUT:   %Generic.assoc_type.d7021d.2: type = assoc_entity_type @Generic, @Generic(%T) [symbolic]
-// CHECK:STDOUT:   %assoc0.31052a.2: %Generic.assoc_type.d7021d.2 = assoc_entity element0, @Generic.WithSelf.%Generic.WithSelf.F.decl [symbolic]
 // CHECK:STDOUT:   %U.as_type: type = facet_access_type %U [symbolic]
 // CHECK:STDOUT:   %pattern_type.70f: type = pattern_type %U.as_type [symbolic]
 // CHECK:STDOUT:   %a.param_patt.98a: %pattern_type.70f = value_param_pattern [symbolic]
@@ -150,6 +145,11 @@ fn B() {
 // CHECK:STDOUT:   %CallGenericMethod: %CallGenericMethod.type = struct_value () [concrete]
 // CHECK:STDOUT:   %require_complete.096: <witness> = require_complete_type %U.as_type [symbolic]
 // CHECK:STDOUT:   %require_complete.944: <witness> = require_complete_type %T [symbolic]
+// CHECK:STDOUT:   %Self.8ea1ea.2: %Generic.type.ee14e9.2 = symbolic_binding Self, 1 [symbolic]
+// CHECK:STDOUT:   %Generic.WithSelf.F.type.390775.2: type = fn_type @Generic.WithSelf.F, @Generic.WithSelf(%T, %Self.8ea1ea.1) [symbolic]
+// CHECK:STDOUT:   %Generic.WithSelf.F.b85a66.2: %Generic.WithSelf.F.type.390775.2 = struct_value () [symbolic]
+// CHECK:STDOUT:   %Generic.assoc_type.d7021d.2: type = assoc_entity_type @Generic, @Generic(%T) [symbolic]
+// CHECK:STDOUT:   %assoc0.31052a.2: %Generic.assoc_type.d7021d.2 = assoc_entity element0, @Generic.WithSelf.%Generic.WithSelf.F.decl [symbolic]
 // CHECK:STDOUT:   %require_complete.13f: <witness> = require_complete_type %Generic.type.ee14e9.2 [symbolic]
 // CHECK:STDOUT:   %Generic.WithSelf.F.type.a70: type = fn_type @Generic.WithSelf.F, @Generic.WithSelf(%T, %U) [symbolic]
 // CHECK:STDOUT:   %Generic.WithSelf.F.5e8: %Generic.WithSelf.F.type.a70 = struct_value () [symbolic]
@@ -446,17 +446,6 @@ fn B() {
 // CHECK:STDOUT:   %Self.loc4_33.2 => constants.%Self.8ea1ea.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific @Generic.WithSelf(constants.%T, constants.%Self.8ea1ea.1) {
-// CHECK:STDOUT: !definition:
-// CHECK:STDOUT:   %Scalar => constants.%T
-// CHECK:STDOUT:   %Generic.type => constants.%Generic.type.ee14e9.2
-// CHECK:STDOUT:   %Self => constants.%Self.8ea1ea.1
-// CHECK:STDOUT:   %Generic.WithSelf.F.type => constants.%Generic.WithSelf.F.type.390775.2
-// CHECK:STDOUT:   %Generic.WithSelf.F => constants.%Generic.WithSelf.F.b85a66.2
-// CHECK:STDOUT:   %Generic.assoc_type => constants.%Generic.assoc_type.d7021d.2
-// CHECK:STDOUT:   %assoc0.loc5_9.2 => constants.%assoc0.31052a.2
-// CHECK:STDOUT: }
-// CHECK:STDOUT:
 // CHECK:STDOUT: specific @CallGenericMethod(constants.%T, constants.%U) {
 // CHECK:STDOUT:   %T.patt.loc15_23.2 => constants.%T.patt
 // CHECK:STDOUT:   %T.loc15_23.1 => constants.%T
@@ -473,6 +462,17 @@ fn B() {
 // CHECK:STDOUT:   %s.patt.loc15_67.2 => constants.%s.patt.a4f
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
+// CHECK:STDOUT: specific @Generic.WithSelf(constants.%T, constants.%Self.8ea1ea.1) {
+// CHECK:STDOUT: !definition:
+// CHECK:STDOUT:   %Scalar => constants.%T
+// CHECK:STDOUT:   %Generic.type => constants.%Generic.type.ee14e9.2
+// CHECK:STDOUT:   %Self => constants.%Self.8ea1ea.1
+// CHECK:STDOUT:   %Generic.WithSelf.F.type => constants.%Generic.WithSelf.F.type.390775.2
+// CHECK:STDOUT:   %Generic.WithSelf.F => constants.%Generic.WithSelf.F.b85a66.2
+// CHECK:STDOUT:   %Generic.assoc_type => constants.%Generic.assoc_type.d7021d.2
+// CHECK:STDOUT:   %assoc0.loc5_9.2 => constants.%assoc0.31052a.2
+// CHECK:STDOUT: }
+// CHECK:STDOUT:
 // CHECK:STDOUT: specific @Generic.WithSelf(constants.%T, constants.%U) {
 // CHECK:STDOUT: !definition:
 // CHECK:STDOUT:   %Scalar => constants.%T
@@ -546,7 +546,6 @@ fn B() {
 // CHECK:STDOUT:   %pattern_type.bd4: type = pattern_type %I.type.722 [concrete]
 // CHECK:STDOUT:   %T.patt.be3: %pattern_type.bd4 = symbolic_binding_pattern T, 0 [symbolic]
 // CHECK:STDOUT:   %T.a08: %I.type.722 = symbolic_binding T, 0 [symbolic]
-// CHECK:STDOUT:   %Self.9e2: %I.type.722 = symbolic_binding Self, 2 [symbolic]
 // CHECK:STDOUT:   %T.as_type: type = facet_access_type %T.a08 [symbolic]
 // CHECK:STDOUT:   %pattern_type.d7b: type = pattern_type %T.as_type [symbolic]
 // CHECK:STDOUT:   %t.param_patt.be8: %pattern_type.d7b = value_param_pattern [symbolic]
@@ -559,6 +558,7 @@ fn B() {
 // CHECK:STDOUT:   %C.val: %C = struct_value () [concrete]
 // CHECK:STDOUT:   %.793: <witness> = impl_self_witness %C, @I, @I(%empty_struct_type, %empty_tuple.type) [concrete]
 // CHECK:STDOUT:   %I.impl_witness.a7c: <witness> = impl_witness @C.as.I.impl.%I.impl_witness_table, @C.as.I.impl(%empty_struct_type) [concrete]
+// CHECK:STDOUT:   %Self.9e2: %I.type.722 = symbolic_binding Self, 2 [symbolic]
 // CHECK:STDOUT:   %complete_type.dfa: <witness> = complete_type_witness %I.type.722 [concrete]
 // CHECK:STDOUT:   %I.facet.831: %I.type.722 = facet_value %C, (%I.impl_witness.a7c) [concrete]
 // CHECK:STDOUT:   %pattern_type.98b: type = pattern_type %C [concrete]
@@ -789,10 +789,6 @@ fn B() {
 // CHECK:STDOUT:   %Self.loc3_31.2 => constants.%Self.9e2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific @I.WithSelf(constants.%empty_struct_type, constants.%empty_tuple.type, constants.%Self.299) {
-// CHECK:STDOUT: !definition:
-// CHECK:STDOUT: }
-// CHECK:STDOUT:
 // CHECK:STDOUT: specific @A(constants.%T.a08) {
 // CHECK:STDOUT:   %T.patt.loc9_7.2 => constants.%T.patt.be3
 // CHECK:STDOUT:   %T.loc9_7.1 => constants.%T.a08
@@ -813,6 +809,10 @@ fn B() {
 // CHECK:STDOUT:   %require_complete => constants.%complete_type.dfa
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
+// CHECK:STDOUT: specific @I.WithSelf(constants.%empty_struct_type, constants.%empty_tuple.type, constants.%Self.299) {
+// CHECK:STDOUT: !definition:
+// CHECK:STDOUT: }
+// CHECK:STDOUT:
 // CHECK:STDOUT: specific @A(constants.%I.facet.831) {
 // CHECK:STDOUT:   %T.patt.loc9_7.2 => constants.%T.patt.be3
 // CHECK:STDOUT:   %T.loc9_7.1 => constants.%I.facet.831
@@ -857,7 +857,6 @@ fn B() {
 // CHECK:STDOUT:   %pattern_type.5c6: type = pattern_type %I.type.6c0 [concrete]
 // CHECK:STDOUT:   %T.patt.c4c: %pattern_type.5c6 = symbolic_binding_pattern T, 0 [symbolic]
 // CHECK:STDOUT:   %T.b75: %I.type.6c0 = symbolic_binding T, 0 [symbolic]
-// CHECK:STDOUT:   %Self.136: %I.type.6c0 = symbolic_binding Self, 2 [symbolic]
 // CHECK:STDOUT:   %T.as_type: type = facet_access_type %T.b75 [symbolic]
 // CHECK:STDOUT:   %pattern_type.67d: type = pattern_type %T.as_type [symbolic]
 // CHECK:STDOUT:   %t.param_patt: %pattern_type.67d = value_param_pattern [symbolic]
@@ -1063,14 +1062,6 @@ fn B() {
 // CHECK:STDOUT:   %V.loc3_14.1 => constants.%empty_struct_type
 // CHECK:STDOUT:   %W.patt.loc3_23.2 => constants.%W.patt
 // CHECK:STDOUT:   %W.loc3_23.1 => constants.%empty_struct_type
-// CHECK:STDOUT:
-// CHECK:STDOUT: !definition:
-// CHECK:STDOUT:   %I.type => constants.%I.type.6c0
-// CHECK:STDOUT:   %Self.loc3_31.2 => constants.%Self.136
-// CHECK:STDOUT: }
-// CHECK:STDOUT:
-// CHECK:STDOUT: specific @I.WithSelf(constants.%empty_struct_type, constants.%empty_struct_type, constants.%Self.299) {
-// CHECK:STDOUT: !definition:
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: specific @A(constants.%T.b75) {
diff --git a/toolchain/check/testdata/facet/convert_facet_value_to_narrowed_facet_type.carbon b/toolchain/check/testdata/facet/convert_facet_value_to_narrowed_facet_type.carbon
index 8df366d4537e..e9da21d11ad0 100644
--- a/toolchain/check/testdata/facet/convert_facet_value_to_narrowed_facet_type.carbon
+++ b/toolchain/check/testdata/facet/convert_facet_value_to_narrowed_facet_type.carbon
@@ -270,13 +270,9 @@ fn CallsWithTypeExplicit(generic U: type) {
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific @Eats.WithSelf(constants.%Self.23e) {
-// CHECK:STDOUT: !definition:
-// CHECK:STDOUT: }
+// CHECK:STDOUT: specific @Eats.WithSelf(constants.%Self.23e) {}
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific @Animal.WithSelf(constants.%Self.f00) {
-// CHECK:STDOUT: !definition:
-// CHECK:STDOUT: }
+// CHECK:STDOUT: specific @Animal.WithSelf(constants.%Self.f00) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: specific @Feed(constants.%T) {
 // CHECK:STDOUT:   %T.patt.loc6_10.2 => constants.%T.patt
@@ -522,17 +518,11 @@ fn CallsWithTypeExplicit(generic U: type) {
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific @Eats.WithSelf(constants.%Self.23e) {
-// CHECK:STDOUT: !definition:
-// CHECK:STDOUT: }
+// CHECK:STDOUT: specific @Eats.WithSelf(constants.%Self.23e) {}
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific @Animal.WithSelf(constants.%Self.f00) {
-// CHECK:STDOUT: !definition:
-// CHECK:STDOUT: }
+// CHECK:STDOUT: specific @Animal.WithSelf(constants.%Self.f00) {}
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific @Tame.WithSelf(constants.%Self.0f0) {
-// CHECK:STDOUT: !definition:
-// CHECK:STDOUT: }
+// CHECK:STDOUT: specific @Tame.WithSelf(constants.%Self.0f0) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: specific @FeedTame(constants.%V) {
 // CHECK:STDOUT:   %V.patt.loc7_14.2 => constants.%V.patt
@@ -822,13 +812,9 @@ fn CallsWithTypeExplicit(generic U: type) {
 // CHECK:STDOUT: !definition:
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific @Animal.WithSelf(constants.%Self.f00) {
-// CHECK:STDOUT: !definition:
-// CHECK:STDOUT: }
+// CHECK:STDOUT: specific @Animal.WithSelf(constants.%Self.f00) {}
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific @Tame.WithSelf(constants.%Self.0f0) {
-// CHECK:STDOUT: !definition:
-// CHECK:STDOUT: }
+// CHECK:STDOUT: specific @Tame.WithSelf(constants.%Self.0f0) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: specific @A.as_type.as.Eats.impl(constants.%A) {
 // CHECK:STDOUT:   %A.patt.loc7_15.2 => constants.%A.patt
@@ -1040,9 +1026,7 @@ fn CallsWithTypeExplicit(generic U: type) {
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific @A.WithSelf(constants.%Self) {
-// CHECK:STDOUT: !definition:
-// CHECK:STDOUT: }
+// CHECK:STDOUT: specific @A.WithSelf(constants.%Self) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: specific @TakesA(constants.%T) {
 // CHECK:STDOUT:   %T.patt.loc7_12.2 => constants.%T.patt
diff --git a/toolchain/check/testdata/facet/convert_facet_value_value_to_blanket_impl.carbon b/toolchain/check/testdata/facet/convert_facet_value_value_to_blanket_impl.carbon
index bade648652a7..c4c3cf131d5b 100644
--- a/toolchain/check/testdata/facet/convert_facet_value_value_to_blanket_impl.carbon
+++ b/toolchain/check/testdata/facet/convert_facet_value_value_to_blanket_impl.carbon
@@ -228,9 +228,7 @@ fn HandleAnimal[T: Animal](a: T) { Feed(a); }
 // CHECK:STDOUT: !definition:
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific @Animal.WithSelf(constants.%Self.f00) {
-// CHECK:STDOUT: !definition:
-// CHECK:STDOUT: }
+// CHECK:STDOUT: specific @Animal.WithSelf(constants.%Self.f00) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: specific @A.as_type.as.Eats.impl(constants.%A) {
 // CHECK:STDOUT:   %A.patt.loc18_15.2 => constants.%A.patt
diff --git a/toolchain/check/testdata/facet/convert_facet_value_value_to_generic_facet_value_value.carbon b/toolchain/check/testdata/facet/convert_facet_value_value_to_generic_facet_value_value.carbon
index 92a9eb5efe01..69838bf0489b 100644
--- a/toolchain/check/testdata/facet/convert_facet_value_value_to_generic_facet_value_value.carbon
+++ b/toolchain/check/testdata/facet/convert_facet_value_value_to_generic_facet_value_value.carbon
@@ -83,7 +83,6 @@ fn F() {
 // CHECK:STDOUT:   %pattern_type.560: type = pattern_type %Eats.type.eb4 [symbolic]
 // CHECK:STDOUT:   %T.patt.02f: %pattern_type.560 = symbolic_binding_pattern T, 1 [symbolic]
 // CHECK:STDOUT:   %T.b01: %Eats.type.eb4 = symbolic_binding T, 1 [symbolic]
-// CHECK:STDOUT:   %Self.377: %Eats.type.eb4 = symbolic_binding Self, 1 [symbolic]
 // CHECK:STDOUT:   %T.as_type.b84: type = facet_access_type %T.b01 [symbolic]
 // CHECK:STDOUT:   %pattern_type.371: type = pattern_type %T.as_type.b84 [symbolic]
 // CHECK:STDOUT:   %e.param_patt.32e: %pattern_type.371 = value_param_pattern [symbolic]
@@ -565,14 +564,6 @@ fn F() {
 // CHECK:STDOUT: specific @Eats(constants.%Food.as_type.bca) {
 // CHECK:STDOUT:   %Food.patt.loc21_20.2 => constants.%Food.patt.d47
 // CHECK:STDOUT:   %Food.loc21_20.1 => constants.%Food.as_type.bca
-// CHECK:STDOUT:
-// CHECK:STDOUT: !definition:
-// CHECK:STDOUT:   %Eats.type => constants.%Eats.type.eb4
-// CHECK:STDOUT:   %Self.loc21_28.2 => constants.%Self.377
-// CHECK:STDOUT: }
-// CHECK:STDOUT:
-// CHECK:STDOUT: specific @Eats.WithSelf(constants.%Food.as_type.bca, constants.%Self.db3) {
-// CHECK:STDOUT: !definition:
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: specific @Feed(constants.%Food.196, constants.%T.b01) {
diff --git a/toolchain/check/testdata/facet/fail_convert_facet_value_to_missing_impl.carbon b/toolchain/check/testdata/facet/fail_convert_facet_value_to_missing_impl.carbon
index 9da26c9230bb..39904fe3fc87 100644
--- a/toolchain/check/testdata/facet/fail_convert_facet_value_to_missing_impl.carbon
+++ b/toolchain/check/testdata/facet/fail_convert_facet_value_to_missing_impl.carbon
@@ -171,13 +171,9 @@ fn HandleAnimal[T: Animal](a: T) { Feed(a); }
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific @Eats.WithSelf(constants.%Self.23e) {
-// CHECK:STDOUT: !definition:
-// CHECK:STDOUT: }
+// CHECK:STDOUT: specific @Eats.WithSelf(constants.%Self.23e) {}
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific @Animal.WithSelf(constants.%Self.f00) {
-// CHECK:STDOUT: !definition:
-// CHECK:STDOUT: }
+// CHECK:STDOUT: specific @Animal.WithSelf(constants.%Self.f00) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: specific @Feed(constants.%T.672) {
 // CHECK:STDOUT:   %T.patt.loc18_10.2 => constants.%T.patt.9e8
diff --git a/toolchain/check/testdata/function/generic/fail_deduce_imported_function.carbon b/toolchain/check/testdata/function/generic/fail_deduce_imported_function.carbon
index eff56c5850db..c2a708582d00 100644
--- a/toolchain/check/testdata/function/generic/fail_deduce_imported_function.carbon
+++ b/toolchain/check/testdata/function/generic/fail_deduce_imported_function.carbon
@@ -121,9 +121,7 @@ fn B() {
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific @Z.WithSelf(constants.%Self) {
-// CHECK:STDOUT: !definition:
-// CHECK:STDOUT: }
+// CHECK:STDOUT: specific @Z.WithSelf(constants.%Self) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: specific @A(constants.%T) {
 // CHECK:STDOUT:   %T.patt.loc4_7.2 => constants.%T.patt
@@ -259,9 +257,7 @@ fn B() {
 // CHECK:STDOUT:   fn;
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific @Z.WithSelf(constants.%Self) {
-// CHECK:STDOUT: !definition:
-// CHECK:STDOUT: }
+// CHECK:STDOUT: specific @Z.WithSelf(constants.%Self) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: specific @A.loc4(constants.%T) {
 // CHECK:STDOUT:   %T.patt.loc4_7.2 => constants.%T.patt
diff --git a/toolchain/check/testdata/impl/generic_redeclaration.carbon b/toolchain/check/testdata/impl/generic_redeclaration.carbon
index 4c8229340036..5568f3b83a72 100644
--- a/toolchain/check/testdata/impl/generic_redeclaration.carbon
+++ b/toolchain/check/testdata/impl/generic_redeclaration.carbon
@@ -434,21 +434,13 @@ impl forall [T: type] T as I {
 // CHECK:STDOUT: !definition:
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific @I.WithSelf(constants.%Self.37e) {
-// CHECK:STDOUT: !definition:
-// CHECK:STDOUT: }
+// CHECK:STDOUT: specific @I.WithSelf(constants.%Self.37e) {}
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific @J.WithSelf(constants.%Self.653) {
-// CHECK:STDOUT: !definition:
-// CHECK:STDOUT: }
+// CHECK:STDOUT: specific @J.WithSelf(constants.%Self.653) {}
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific @K.WithSelf(constants.%Self.a32) {
-// CHECK:STDOUT: !definition:
-// CHECK:STDOUT: }
+// CHECK:STDOUT: specific @K.WithSelf(constants.%Self.a32) {}
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific @L.WithSelf(constants.%Self.480) {
-// CHECK:STDOUT: !definition:
-// CHECK:STDOUT: }
+// CHECK:STDOUT: specific @L.WithSelf(constants.%Self.480) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: specific @T.as_type.as.Interface.impl.72f(constants.%T.dda) {
 // CHECK:STDOUT:   %T.patt.loc12_15.2 => constants.%T.patt.1df
@@ -618,9 +610,7 @@ impl forall [T: type] T as I {
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific @I.WithSelf(constants.%Self.37e) {
-// CHECK:STDOUT: !definition:
-// CHECK:STDOUT: }
+// CHECK:STDOUT: specific @I.WithSelf(constants.%Self.37e) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: specific @J.WithSelf(constants.%Self.653) {
 // CHECK:STDOUT: !definition:
diff --git a/toolchain/check/testdata/impl/impl_as_named_constraint.carbon b/toolchain/check/testdata/impl/impl_as_named_constraint.carbon
index b6feb7771ae1..d127f975add8 100644
--- a/toolchain/check/testdata/impl/impl_as_named_constraint.carbon
+++ b/toolchain/check/testdata/impl/impl_as_named_constraint.carbon
@@ -313,6 +313,34 @@ constraint Y {
 // CHECK:STDERR:
 impl () as Y {}
 
+// --- fail_todo_member_access_in_extend_require.carbon
+library "[[@TEST_NAME]]";
+
+interface I { let X: type; }
+interface J {}
+
+impl () as J {}
+
+constraint GivesI {
+  extend require impls I where .X impls J;
+}
+
+// When we check this we check that GivesI is complete, which:
+// - Forms the self-specific for GivesI's extend require
+// - Creates Self.(I.X) which has a LookupImplWitness for `Self as I`
+// - Evaluates the witness which finds this impl
+// - Deduces for Self which tries to convert Self to type
+// - Requires the type of Self to be complete, and its type is GivesI
+// - Forms the self-specfic for GivesI's extend require....we have a loop.
+//
+// TODO: .X = () should satisfy the requirement that .X impls J. We're not
+// finding the rewrite when checking requirements.
+// CHECK:STDERR: fail_todo_member_access_in_extend_require.carbon:[[@LINE+4]]:1: error: constraint `GivesI where .(I.X) = ()` being implemented requires that `T.(I.X)` implements `J` [IdentifiedRequireImplsNotImplemented]
+// CHECK:STDERR: impl forall [T: type] T as GivesI where .X = () {}
+// CHECK:STDERR: ^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+// CHECK:STDERR:
+impl forall [T: type] T as GivesI where .X = () {}
+
 // CHECK:STDOUT: --- fail_error_self_in_require.carbon
 // CHECK:STDOUT:
 // CHECK:STDOUT: constants {
diff --git a/toolchain/check/testdata/interface/fail_member_lookup.carbon b/toolchain/check/testdata/interface/fail_member_lookup.carbon
index 38932dc91ef0..ff815c84cc35 100644
--- a/toolchain/check/testdata/interface/fail_member_lookup.carbon
+++ b/toolchain/check/testdata/interface/fail_member_lookup.carbon
@@ -184,9 +184,7 @@ fn G(generic U: Different) -> U.(Interface.T);
 // CHECK:STDOUT:
 // CHECK:STDOUT: specific @Interface.WithSelf.F(constants.%Self.3ce) {}
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific @Different.WithSelf(constants.%Self.8ba) {
-// CHECK:STDOUT: !definition:
-// CHECK:STDOUT: }
+// CHECK:STDOUT: specific @Different.WithSelf(constants.%Self.8ba) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: specific @G(constants.%U) {
 // CHECK:STDOUT:   %U.patt.loc32_15.2 => constants.%U.patt
diff --git a/toolchain/check/testdata/interface/generic.carbon b/toolchain/check/testdata/interface/generic.carbon
index fa78c45a0948..74d4f7e84574 100644
--- a/toolchain/check/testdata/interface/generic.carbon
+++ b/toolchain/check/testdata/interface/generic.carbon
@@ -484,7 +484,7 @@ fn F(unused generic T: Generic((), ())) {}
 // CHECK:STDOUT:   %Generic.type.30d: type = generic_interface_type @Generic [concrete]
 // CHECK:STDOUT:   %Generic.generic: %Generic.type.30d = struct_value () [concrete]
 // CHECK:STDOUT:   %Generic.type.ee1: type = facet_type <@Generic, @Generic(%T.67d)> [symbolic]
-// CHECK:STDOUT:   %Self.8ea: %Generic.type.ee1 = symbolic_binding Self, 1 [symbolic]
+// CHECK:STDOUT:   %Self: %Generic.type.ee1 = symbolic_binding Self, 1 [symbolic]
 // CHECK:STDOUT:   %A: type = class_type @A [concrete]
 // CHECK:STDOUT:   %empty_struct_type: type = struct_type {} [concrete]
 // CHECK:STDOUT:   %complete_type: <witness> = complete_type_witness %empty_struct_type [concrete]
@@ -501,7 +501,6 @@ fn F(unused generic T: Generic((), ())) {}
 // CHECK:STDOUT:   %T.f18: %Generic.type.57d = symbolic_binding T, 0 [symbolic]
 // CHECK:STDOUT:   %G.type: type = fn_type @G [concrete]
 // CHECK:STDOUT:   %G: %G.type = struct_value () [concrete]
-// CHECK:STDOUT:   %Self.cb2: %Generic.type.57d = symbolic_binding Self, 1 [symbolic]
 // CHECK:STDOUT:   %T.as_type: type = facet_access_type %T.f18 [symbolic]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -554,10 +553,10 @@ fn F(unused generic T: Generic((), ())) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: !definition:
 // CHECK:STDOUT:   %Generic.type: type = facet_type <@Generic, @Generic(%T.loc4_20.1)> [symbolic = %Generic.type (constants.%Generic.type.ee1)]
-// CHECK:STDOUT:   %Self.loc4_28.2: @Generic.%Generic.type (%Generic.type.ee1) = symbolic_binding Self, 1 [symbolic = %Self.loc4_28.2 (constants.%Self.8ea)]
+// CHECK:STDOUT:   %Self.loc4_28.2: @Generic.%Generic.type (%Generic.type.ee1) = symbolic_binding Self, 1 [symbolic = %Self.loc4_28.2 (constants.%Self)]
 // CHECK:STDOUT:
 // CHECK:STDOUT:   interface {
-// CHECK:STDOUT:     %Self.loc4_28.1: @Generic.%Generic.type (%Generic.type.ee1) = symbolic_binding Self, 1 [symbolic = %Self.loc4_28.2 (constants.%Self.8ea)]
+// CHECK:STDOUT:     %Self.loc4_28.1: @Generic.%Generic.type (%Generic.type.ee1) = symbolic_binding Self, 1 [symbolic = %Self.loc4_28.2 (constants.%Self)]
 // CHECK:STDOUT:     %Generic.WithSelf.decl = interface_with_self_decl @Generic [concrete]
 // CHECK:STDOUT:
 // CHECK:STDOUT:   !members:
@@ -612,7 +611,7 @@ fn F(unused generic T: Generic((), ())) {}
 // CHECK:STDOUT:   %T.loc4_20.1 => constants.%T.67d
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific @Generic.WithSelf(constants.%T.67d, constants.%Self.8ea) {}
+// CHECK:STDOUT: specific @Generic.WithSelf(constants.%T.67d, constants.%Self) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: specific @Generic(constants.%A) {
 // CHECK:STDOUT:   %T.patt.loc4_20.2 => constants.%T.patt.d47
@@ -627,10 +626,6 @@ fn F(unused generic T: Generic((), ())) {}
 // CHECK:STDOUT: specific @Generic(constants.%B) {
 // CHECK:STDOUT:   %T.patt.loc4_20.2 => constants.%T.patt.d47
 // CHECK:STDOUT:   %T.loc4_20.1 => constants.%B
-// CHECK:STDOUT:
-// CHECK:STDOUT: !definition:
-// CHECK:STDOUT:   %Generic.type => constants.%Generic.type.57d
-// CHECK:STDOUT:   %Self.loc4_28.2 => constants.%Self.cb2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: specific @G(constants.%T.f18) {
@@ -638,10 +633,6 @@ fn F(unused generic T: Generic((), ())) {}
 // CHECK:STDOUT:   %T.loc10_15.1 => constants.%T.f18
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific @Generic.WithSelf(constants.%B, constants.%Self.8ea) {
-// CHECK:STDOUT: !definition:
-// CHECK:STDOUT: }
-// CHECK:STDOUT:
 // CHECK:STDOUT: --- fail_args_count_mismatch.carbon
 // CHECK:STDOUT:
 // CHECK:STDOUT: constants {
diff --git a/toolchain/check/testdata/interface/require.carbon b/toolchain/check/testdata/interface/require.carbon
index d688a6ac9e2c..42c2ceac0283 100644
--- a/toolchain/check/testdata/interface/require.carbon
+++ b/toolchain/check/testdata/interface/require.carbon
@@ -552,9 +552,7 @@ interface Z(T: type) {
 // CHECK:STDOUT:   %Self.as_type.loc9_11.2: type = facet_access_type %Self [symbolic = %Self.as_type.loc9_11.2 (constants.%Self.as_type)]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific @Z.WithSelf(constants.%Self.cb6) {
-// CHECK:STDOUT: !definition:
-// CHECK:STDOUT: }
+// CHECK:STDOUT: specific @Z.WithSelf(constants.%Self.cb6) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: specific @Z.WithSelf.Self.as_type.impls.Y.type.require(constants.%Self.cb6) {
 // CHECK:STDOUT:   %Self => constants.%Self.cb6
@@ -605,9 +603,7 @@ interface Z(T: type) {
 // CHECK:STDOUT:   %Self.as_type.loc9_11.2: type = facet_access_type %Self [symbolic = %Self.as_type.loc9_11.2 (constants.%Self.as_type)]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific @Z.WithSelf(constants.%Self.cb6) {
-// CHECK:STDOUT: !definition:
-// CHECK:STDOUT: }
+// CHECK:STDOUT: specific @Z.WithSelf(constants.%Self.cb6) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: specific @Z.WithSelf.Self.as_type.impls.Y.type.require(constants.%Self.cb6) {
 // CHECK:STDOUT:   %Self => constants.%Self.cb6
diff --git a/toolchain/check/testdata/interop/cpp/function/import/overloads.carbon b/toolchain/check/testdata/interop/cpp/function/import/overloads.carbon
index e080ad077ebe..6fd3cf2e244b 100644
--- a/toolchain/check/testdata/interop/cpp/function/import/overloads.carbon
+++ b/toolchain/check/testdata/interop/cpp/function/import/overloads.carbon
@@ -4069,9 +4069,7 @@ fn F() {
 // CHECK:STDOUT:   return
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific @I.WithSelf(constants.%Self) {
-// CHECK:STDOUT: !definition:
-// CHECK:STDOUT: }
+// CHECK:STDOUT: specific @I.WithSelf(constants.%Self) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: specific @EchoValue(constants.%ValueT, constants.%value) {
 // CHECK:STDOUT:   %ValueT.patt.loc10_20.2 => constants.%ValueT.patt
diff --git a/toolchain/check/testdata/interop/cpp/operators/arithmetic_operators.carbon b/toolchain/check/testdata/interop/cpp/operators/arithmetic_operators.carbon
index 2b3064f6e09c..10ed4b4d5942 100644
--- a/toolchain/check/testdata/interop/cpp/operators/arithmetic_operators.carbon
+++ b/toolchain/check/testdata/interop/cpp/operators/arithmetic_operators.carbon
@@ -1059,8 +1059,6 @@ fn TestUnaryOperators(a: Cpp.Int16, b: Cpp.Int32) {
 // CHECK:STDOUT:   %pattern_type.82d: type = pattern_type %AddAssignWith.type.2c8890.2 [symbolic]
 // CHECK:STDOUT:   %T.patt.a22: %pattern_type.82d = symbolic_binding_pattern T, 1 [symbolic]
 // CHECK:STDOUT:   %T.792: %AddAssignWith.type.2c8890.2 = symbolic_binding T, 1 [symbolic]
-// CHECK:STDOUT:   %AddAssignWith.assoc_type.8ddaf4.2: type = assoc_entity_type @AddAssignWith.1, @AddAssignWith.1(%U.67d) [symbolic]
-// CHECK:STDOUT:   %assoc0.8c5739.2: %AddAssignWith.assoc_type.8ddaf4.2 = assoc_entity element0, imports.%Core.import_ref.3b2 [symbolic]
 // CHECK:STDOUT:   %T.as_type.50c: type = facet_access_type %T.792 [symbolic]
 // CHECK:STDOUT:   %pattern_type.643306.2: type = pattern_type %T.as_type.50c [symbolic]
 // CHECK:STDOUT:   %x.patt.227: %pattern_type.643306.2 = ref_binding_pattern x [symbolic]
@@ -1068,6 +1066,8 @@ fn TestUnaryOperators(a: Cpp.Int16, b: Cpp.Int32) {
 // CHECK:STDOUT:   %pattern_type.51d1c4.4: type = pattern_type %U.67d [symbolic]
 // CHECK:STDOUT:   %y.param_patt.be3: %pattern_type.51d1c4.4 = value_param_pattern [symbolic]
 // CHECK:STDOUT:   %y.patt.b85: %pattern_type.51d1c4.4 = at_binding_pattern y, %y.param_patt.be3 [symbolic]
+// CHECK:STDOUT:   %AddAssignWith.assoc_type.8ddaf4.2: type = assoc_entity_type @AddAssignWith.1, @AddAssignWith.1(%U.67d) [symbolic]
+// CHECK:STDOUT:   %assoc0.8c5739.2: %AddAssignWith.assoc_type.8ddaf4.2 = assoc_entity element0, imports.%Core.import_ref.3b2 [symbolic]
 // CHECK:STDOUT:   %require_complete.2a8: <witness> = require_complete_type %AddAssignWith.type.2c8890.2 [symbolic]
 // CHECK:STDOUT:   %assoc0.86d: %AddAssignWith.assoc_type.8ddaf4.1 = assoc_entity element0, imports.%Core.import_ref.87e [symbolic]
 // CHECK:STDOUT:   %AddAssignWith.lookup_impl_witness: <witness> = lookup_impl_witness %T.792, @AddAssignWith.1, @AddAssignWith.1(%U.67d) [symbolic]
@@ -1084,12 +1084,12 @@ fn TestUnaryOperators(a: Cpp.Int16, b: Cpp.Int32) {
 // CHECK:STDOUT:   %pattern_type.260: type = pattern_type %SubAssignWith.type.7e53cf.2 [symbolic]
 // CHECK:STDOUT:   %T.patt.f45: %pattern_type.260 = symbolic_binding_pattern T, 1 [symbolic]
 // CHECK:STDOUT:   %T.f6c: %SubAssignWith.type.7e53cf.2 = symbolic_binding T, 1 [symbolic]
-// CHECK:STDOUT:   %SubAssignWith.assoc_type.6e3877.2: type = assoc_entity_type @SubAssignWith.1, @SubAssignWith.1(%U.67d) [symbolic]
-// CHECK:STDOUT:   %assoc0.701e5f.2: %SubAssignWith.assoc_type.6e3877.2 = assoc_entity element0, imports.%Core.import_ref.8f2 [symbolic]
 // CHECK:STDOUT:   %T.as_type.3ff: type = facet_access_type %T.f6c [symbolic]
 // CHECK:STDOUT:   %pattern_type.f08ed5.2: type = pattern_type %T.as_type.3ff [symbolic]
 // CHECK:STDOUT:   %x.patt.95a: %pattern_type.f08ed5.2 = ref_binding_pattern x [symbolic]
 // CHECK:STDOUT:   %x.param_patt.a45: %pattern_type.f08ed5.2 = var_param_pattern %x.patt.95a [symbolic]
+// CHECK:STDOUT:   %SubAssignWith.assoc_type.6e3877.2: type = assoc_entity_type @SubAssignWith.1, @SubAssignWith.1(%U.67d) [symbolic]
+// CHECK:STDOUT:   %assoc0.701e5f.2: %SubAssignWith.assoc_type.6e3877.2 = assoc_entity element0, imports.%Core.import_ref.8f2 [symbolic]
 // CHECK:STDOUT:   %require_complete.862: <witness> = require_complete_type %SubAssignWith.type.7e53cf.2 [symbolic]
 // CHECK:STDOUT:   %assoc0.b8e: %SubAssignWith.assoc_type.6e3877.1 = assoc_entity element0, imports.%Core.import_ref.e7f [symbolic]
 // CHECK:STDOUT:   %SubAssignWith.lookup_impl_witness: <witness> = lookup_impl_witness %T.f6c, @SubAssignWith.1, @SubAssignWith.1(%U.67d) [symbolic]
@@ -1106,12 +1106,12 @@ fn TestUnaryOperators(a: Cpp.Int16, b: Cpp.Int32) {
 // CHECK:STDOUT:   %pattern_type.8c2: type = pattern_type %MulAssignWith.type.3a0e4d.2 [symbolic]
 // CHECK:STDOUT:   %T.patt.db5: %pattern_type.8c2 = symbolic_binding_pattern T, 1 [symbolic]
 // CHECK:STDOUT:   %T.64d: %MulAssignWith.type.3a0e4d.2 = symbolic_binding T, 1 [symbolic]
-// CHECK:STDOUT:   %MulAssignWith.assoc_type.9aa18f.2: type = assoc_entity_type @MulAssignWith.1, @MulAssignWith.1(%U.67d) [symbolic]
-// CHECK:STDOUT:   %assoc0.22264a.2: %MulAssignWith.assoc_type.9aa18f.2 = assoc_entity element0, imports.%Core.import_ref.ba3 [symbolic]
 // CHECK:STDOUT:   %T.as_type.1de: type = facet_access_type %T.64d [symbolic]
 // CHECK:STDOUT:   %pattern_type.8bf366.2: type = pattern_type %T.as_type.1de [symbolic]
 // CHECK:STDOUT:   %x.patt.4e9: %pattern_type.8bf366.2 = ref_binding_pattern x [symbolic]
 // CHECK:STDOUT:   %x.param_patt.6c8: %pattern_type.8bf366.2 = var_param_pattern %x.patt.4e9 [symbolic]
+// CHECK:STDOUT:   %MulAssignWith.assoc_type.9aa18f.2: type = assoc_entity_type @MulAssignWith.1, @MulAssignWith.1(%U.67d) [symbolic]
+// CHECK:STDOUT:   %assoc0.22264a.2: %MulAssignWith.assoc_type.9aa18f.2 = assoc_entity element0, imports.%Core.import_ref.ba3 [symbolic]
 // CHECK:STDOUT:   %require_complete.6b1: <witness> = require_complete_type %MulAssignWith.type.3a0e4d.2 [symbolic]
 // CHECK:STDOUT:   %assoc0.2ec: %MulAssignWith.assoc_type.9aa18f.1 = assoc_entity element0, imports.%Core.import_ref.408 [symbolic]
 // CHECK:STDOUT:   %MulAssignWith.lookup_impl_witness: <witness> = lookup_impl_witness %T.64d, @MulAssignWith.1, @MulAssignWith.1(%U.67d) [symbolic]
@@ -1128,12 +1128,12 @@ fn TestUnaryOperators(a: Cpp.Int16, b: Cpp.Int32) {
 // CHECK:STDOUT:   %pattern_type.f74: type = pattern_type %DivAssignWith.type.7e58ca.2 [symbolic]
 // CHECK:STDOUT:   %T.patt.9a5: %pattern_type.f74 = symbolic_binding_pattern T, 1 [symbolic]
 // CHECK:STDOUT:   %T.c33: %DivAssignWith.type.7e58ca.2 = symbolic_binding T, 1 [symbolic]
-// CHECK:STDOUT:   %DivAssignWith.assoc_type.bb68ec.2: type = assoc_entity_type @DivAssignWith.1, @DivAssignWith.1(%U.67d) [symbolic]
-// CHECK:STDOUT:   %assoc0.32f100.2: %DivAssignWith.assoc_type.bb68ec.2 = assoc_entity element0, imports.%Core.import_ref.a5d [symbolic]
 // CHECK:STDOUT:   %T.as_type.e57: type = facet_access_type %T.c33 [symbolic]
 // CHECK:STDOUT:   %pattern_type.da303b.2: type = pattern_type %T.as_type.e57 [symbolic]
 // CHECK:STDOUT:   %x.patt.cf6: %pattern_type.da303b.2 = ref_binding_pattern x [symbolic]
 // CHECK:STDOUT:   %x.param_patt.660: %pattern_type.da303b.2 = var_param_pattern %x.patt.cf6 [symbolic]
+// CHECK:STDOUT:   %DivAssignWith.assoc_type.bb68ec.2: type = assoc_entity_type @DivAssignWith.1, @DivAssignWith.1(%U.67d) [symbolic]
+// CHECK:STDOUT:   %assoc0.32f100.2: %DivAssignWith.assoc_type.bb68ec.2 = assoc_entity element0, imports.%Core.import_ref.a5d [symbolic]
 // CHECK:STDOUT:   %require_complete.c5c: <witness> = require_complete_type %DivAssignWith.type.7e58ca.2 [symbolic]
 // CHECK:STDOUT:   %assoc0.de1: %DivAssignWith.assoc_type.bb68ec.1 = assoc_entity element0, imports.%Core.import_ref.df2 [symbolic]
 // CHECK:STDOUT:   %DivAssignWith.lookup_impl_witness: <witness> = lookup_impl_witness %T.c33, @DivAssignWith.1, @DivAssignWith.1(%U.67d) [symbolic]
@@ -1150,12 +1150,12 @@ fn TestUnaryOperators(a: Cpp.Int16, b: Cpp.Int32) {
 // CHECK:STDOUT:   %pattern_type.fb8: type = pattern_type %ModAssignWith.type.778d68.2 [symbolic]
 // CHECK:STDOUT:   %T.patt.c29: %pattern_type.fb8 = symbolic_binding_pattern T, 1 [symbolic]
 // CHECK:STDOUT:   %T.bca: %ModAssignWith.type.778d68.2 = symbolic_binding T, 1 [symbolic]
-// CHECK:STDOUT:   %ModAssignWith.assoc_type.bc79ec.2: type = assoc_entity_type @ModAssignWith.1, @ModAssignWith.1(%U.67d) [symbolic]
-// CHECK:STDOUT:   %assoc0.8c0719.2: %ModAssignWith.assoc_type.bc79ec.2 = assoc_entity element0, imports.%Core.import_ref.cf6 [symbolic]
 // CHECK:STDOUT:   %T.as_type.ce6: type = facet_access_type %T.bca [symbolic]
 // CHECK:STDOUT:   %pattern_type.1d5f30.2: type = pattern_type %T.as_type.ce6 [symbolic]
 // CHECK:STDOUT:   %x.patt.fa4: %pattern_type.1d5f30.2 = ref_binding_pattern x [symbolic]
 // CHECK:STDOUT:   %x.param_patt.749: %pattern_type.1d5f30.2 = var_param_pattern %x.patt.fa4 [symbolic]
+// CHECK:STDOUT:   %ModAssignWith.assoc_type.bc79ec.2: type = assoc_entity_type @ModAssignWith.1, @ModAssignWith.1(%U.67d) [symbolic]
+// CHECK:STDOUT:   %assoc0.8c0719.2: %ModAssignWith.assoc_type.bc79ec.2 = assoc_entity element0, imports.%Core.import_ref.cf6 [symbolic]
 // CHECK:STDOUT:   %require_complete.680: <witness> = require_complete_type %ModAssignWith.type.778d68.2 [symbolic]
 // CHECK:STDOUT:   %assoc0.0f3: %ModAssignWith.assoc_type.bc79ec.1 = assoc_entity element0, imports.%Core.import_ref.d29 [symbolic]
 // CHECK:STDOUT:   %ModAssignWith.lookup_impl_witness: <witness> = lookup_impl_witness %T.bca, @ModAssignWith.1, @ModAssignWith.1(%U.67d) [symbolic]
diff --git a/toolchain/check/testdata/interop/cpp/operators/eq_with.carbon b/toolchain/check/testdata/interop/cpp/operators/eq_with.carbon
index a190ec47a89d..86e4c0597261 100644
--- a/toolchain/check/testdata/interop/cpp/operators/eq_with.carbon
+++ b/toolchain/check/testdata/interop/cpp/operators/eq_with.carbon
@@ -375,9 +375,6 @@ fn Test(only_neq: Cpp.OnlyNeq,
 // CHECK:STDOUT:   %pattern_type.3d4: type = pattern_type %EqWith.type.98ea86.2 [symbolic]
 // CHECK:STDOUT:   %T.patt.6b9: %pattern_type.3d4 = symbolic_binding_pattern T, 1 [symbolic]
 // CHECK:STDOUT:   %T: %EqWith.type.98ea86.2 = symbolic_binding T, 1 [symbolic]
-// CHECK:STDOUT:   %EqWith.assoc_type.85b122.2: type = assoc_entity_type @EqWith.1, @EqWith.1(%U) [symbolic]
-// CHECK:STDOUT:   %assoc0.eee873.2: %EqWith.assoc_type.85b122.2 = assoc_entity element0, imports.%Core.import_ref.5ba [symbolic]
-// CHECK:STDOUT:   %assoc1.0ffc88.2: %EqWith.assoc_type.85b122.2 = assoc_entity element1, imports.%Core.import_ref.03f [symbolic]
 // CHECK:STDOUT:   %T.as_type: type = facet_access_type %T [symbolic]
 // CHECK:STDOUT:   %pattern_type.e6374a.2: type = pattern_type %T.as_type [symbolic]
 // CHECK:STDOUT:   %x.param_patt.aa2: %pattern_type.e6374a.2 = value_param_pattern [symbolic]
@@ -385,6 +382,9 @@ fn Test(only_neq: Cpp.OnlyNeq,
 // CHECK:STDOUT:   %pattern_type.51d1c4.2: type = pattern_type %U [symbolic]
 // CHECK:STDOUT:   %y.param_patt.be3: %pattern_type.51d1c4.2 = value_param_pattern [symbolic]
 // CHECK:STDOUT:   %y.patt.b85: %pattern_type.51d1c4.2 = at_binding_pattern y, %y.param_patt.be3 [symbolic]
+// CHECK:STDOUT:   %EqWith.assoc_type.85b122.2: type = assoc_entity_type @EqWith.1, @EqWith.1(%U) [symbolic]
+// CHECK:STDOUT:   %assoc0.eee873.2: %EqWith.assoc_type.85b122.2 = assoc_entity element0, imports.%Core.import_ref.5ba [symbolic]
+// CHECK:STDOUT:   %assoc1.0ffc88.2: %EqWith.assoc_type.85b122.2 = assoc_entity element1, imports.%Core.import_ref.03f [symbolic]
 // CHECK:STDOUT:   %require_complete.fb5: <witness> = require_complete_type %EqWith.type.98ea86.2 [symbolic]
 // CHECK:STDOUT:   %assoc0.d00: %EqWith.assoc_type.85b122.1 = assoc_entity element0, imports.%Core.import_ref.2e5 [symbolic]
 // CHECK:STDOUT:   %EqWith.lookup_impl_witness: <witness> = lookup_impl_witness %T, @EqWith.1, @EqWith.1(%U) [symbolic]
@@ -545,9 +545,6 @@ fn Test(only_neq: Cpp.OnlyNeq,
 // CHECK:STDOUT:   %pattern_type.3d4: type = pattern_type %EqWith.type.98ea86.2 [symbolic]
 // CHECK:STDOUT:   %T.patt.6b9: %pattern_type.3d4 = symbolic_binding_pattern T, 1 [symbolic]
 // CHECK:STDOUT:   %T: %EqWith.type.98ea86.2 = symbolic_binding T, 1 [symbolic]
-// CHECK:STDOUT:   %EqWith.assoc_type.85b122.2: type = assoc_entity_type @EqWith.1, @EqWith.1(%U) [symbolic]
-// CHECK:STDOUT:   %assoc0.eee873.2: %EqWith.assoc_type.85b122.2 = assoc_entity element0, imports.%Core.import_ref.5ba [symbolic]
-// CHECK:STDOUT:   %assoc1.0ffc88.2: %EqWith.assoc_type.85b122.2 = assoc_entity element1, imports.%Core.import_ref.03f [symbolic]
 // CHECK:STDOUT:   %T.as_type: type = facet_access_type %T [symbolic]
 // CHECK:STDOUT:   %pattern_type.e6374a.2: type = pattern_type %T.as_type [symbolic]
 // CHECK:STDOUT:   %x.param_patt.aa2: %pattern_type.e6374a.2 = value_param_pattern [symbolic]
@@ -555,6 +552,9 @@ fn Test(only_neq: Cpp.OnlyNeq,
 // CHECK:STDOUT:   %pattern_type.51d1c4.2: type = pattern_type %U [symbolic]
 // CHECK:STDOUT:   %y.param_patt.be3: %pattern_type.51d1c4.2 = value_param_pattern [symbolic]
 // CHECK:STDOUT:   %y.patt.b85: %pattern_type.51d1c4.2 = at_binding_pattern y, %y.param_patt.be3 [symbolic]
+// CHECK:STDOUT:   %EqWith.assoc_type.85b122.2: type = assoc_entity_type @EqWith.1, @EqWith.1(%U) [symbolic]
+// CHECK:STDOUT:   %assoc0.eee873.2: %EqWith.assoc_type.85b122.2 = assoc_entity element0, imports.%Core.import_ref.5ba [symbolic]
+// CHECK:STDOUT:   %assoc1.0ffc88.2: %EqWith.assoc_type.85b122.2 = assoc_entity element1, imports.%Core.import_ref.03f [symbolic]
 // CHECK:STDOUT:   %require_complete.fb5: <witness> = require_complete_type %EqWith.type.98ea86.2 [symbolic]
 // CHECK:STDOUT:   %assoc0.d00: %EqWith.assoc_type.85b122.1 = assoc_entity element0, imports.%Core.import_ref.2e5 [symbolic]
 // CHECK:STDOUT:   %EqWith.lookup_impl_witness: <witness> = lookup_impl_witness %T, @EqWith.1, @EqWith.1(%U) [symbolic]
diff --git a/toolchain/check/testdata/interop/cpp/operators/ordered_with.carbon b/toolchain/check/testdata/interop/cpp/operators/ordered_with.carbon
index 1d872d2c2683..e8eeffdbbe80 100644
--- a/toolchain/check/testdata/interop/cpp/operators/ordered_with.carbon
+++ b/toolchain/check/testdata/interop/cpp/operators/ordered_with.carbon
@@ -411,11 +411,6 @@ fn Test(missing_less: Cpp.MissingLess,
 // CHECK:STDOUT:   %pattern_type.ebc: type = pattern_type %OrderedWith.type.32ae87.2 [symbolic]
 // CHECK:STDOUT:   %T.patt.aaa: %pattern_type.ebc = symbolic_binding_pattern T, 1 [symbolic]
 // CHECK:STDOUT:   %T: %OrderedWith.type.32ae87.2 = symbolic_binding T, 1 [symbolic]
-// CHECK:STDOUT:   %OrderedWith.assoc_type.1d2e6f.2: type = assoc_entity_type @OrderedWith.1, @OrderedWith.1(%U) [symbolic]
-// CHECK:STDOUT:   %assoc0.c0023b.2: %OrderedWith.assoc_type.1d2e6f.2 = assoc_entity element0, imports.%Core.import_ref.e7a [symbolic]
-// CHECK:STDOUT:   %assoc1.3efd77.2: %OrderedWith.assoc_type.1d2e6f.2 = assoc_entity element1, imports.%Core.import_ref.3f7 [symbolic]
-// CHECK:STDOUT:   %assoc2.48eff0.2: %OrderedWith.assoc_type.1d2e6f.2 = assoc_entity element2, imports.%Core.import_ref.385 [symbolic]
-// CHECK:STDOUT:   %assoc3.5d53f7.2: %OrderedWith.assoc_type.1d2e6f.2 = assoc_entity element3, imports.%Core.import_ref.39b [symbolic]
 // CHECK:STDOUT:   %T.as_type: type = facet_access_type %T [symbolic]
 // CHECK:STDOUT:   %pattern_type.f6ec4f.2: type = pattern_type %T.as_type [symbolic]
 // CHECK:STDOUT:   %x.param_patt.a58: %pattern_type.f6ec4f.2 = value_param_pattern [symbolic]
@@ -423,6 +418,11 @@ fn Test(missing_less: Cpp.MissingLess,
 // CHECK:STDOUT:   %pattern_type.51d1c4.2: type = pattern_type %U [symbolic]
 // CHECK:STDOUT:   %y.param_patt.be3: %pattern_type.51d1c4.2 = value_param_pattern [symbolic]
 // CHECK:STDOUT:   %y.patt.b85: %pattern_type.51d1c4.2 = at_binding_pattern y, %y.param_patt.be3 [symbolic]
+// CHECK:STDOUT:   %OrderedWith.assoc_type.1d2e6f.2: type = assoc_entity_type @OrderedWith.1, @OrderedWith.1(%U) [symbolic]
+// CHECK:STDOUT:   %assoc0.c0023b.2: %OrderedWith.assoc_type.1d2e6f.2 = assoc_entity element0, imports.%Core.import_ref.e7a [symbolic]
+// CHECK:STDOUT:   %assoc1.3efd77.2: %OrderedWith.assoc_type.1d2e6f.2 = assoc_entity element1, imports.%Core.import_ref.3f7 [symbolic]
+// CHECK:STDOUT:   %assoc2.48eff0.2: %OrderedWith.assoc_type.1d2e6f.2 = assoc_entity element2, imports.%Core.import_ref.385 [symbolic]
+// CHECK:STDOUT:   %assoc3.5d53f7.2: %OrderedWith.assoc_type.1d2e6f.2 = assoc_entity element3, imports.%Core.import_ref.39b [symbolic]
 // CHECK:STDOUT:   %require_complete.3c0: <witness> = require_complete_type %OrderedWith.type.32ae87.2 [symbolic]
 // CHECK:STDOUT:   %assoc0.13c: %OrderedWith.assoc_type.1d2e6f.1 = assoc_entity element0, imports.%Core.import_ref.447 [symbolic]
 // CHECK:STDOUT:   %OrderedWith.lookup_impl_witness: <witness> = lookup_impl_witness %T, @OrderedWith.1, @OrderedWith.1(%U) [symbolic]
@@ -653,11 +653,6 @@ fn Test(missing_less: Cpp.MissingLess,
 // CHECK:STDOUT:   %pattern_type.ebc: type = pattern_type %OrderedWith.type.32ae87.2 [symbolic]
 // CHECK:STDOUT:   %T.patt.aaa: %pattern_type.ebc = symbolic_binding_pattern T, 1 [symbolic]
 // CHECK:STDOUT:   %T: %OrderedWith.type.32ae87.2 = symbolic_binding T, 1 [symbolic]
-// CHECK:STDOUT:   %OrderedWith.assoc_type.1d2e6f.2: type = assoc_entity_type @OrderedWith.1, @OrderedWith.1(%U) [symbolic]
-// CHECK:STDOUT:   %assoc0.c0023b.2: %OrderedWith.assoc_type.1d2e6f.2 = assoc_entity element0, imports.%Core.import_ref.e7a [symbolic]
-// CHECK:STDOUT:   %assoc1.3efd77.2: %OrderedWith.assoc_type.1d2e6f.2 = assoc_entity element1, imports.%Core.import_ref.3f7 [symbolic]
-// CHECK:STDOUT:   %assoc2.48eff0.2: %OrderedWith.assoc_type.1d2e6f.2 = assoc_entity element2, imports.%Core.import_ref.385 [symbolic]
-// CHECK:STDOUT:   %assoc3.5d53f7.2: %OrderedWith.assoc_type.1d2e6f.2 = assoc_entity element3, imports.%Core.import_ref.39b [symbolic]
 // CHECK:STDOUT:   %T.as_type: type = facet_access_type %T [symbolic]
 // CHECK:STDOUT:   %pattern_type.f6ec4f.2: type = pattern_type %T.as_type [symbolic]
 // CHECK:STDOUT:   %x.param_patt.a58: %pattern_type.f6ec4f.2 = value_param_pattern [symbolic]
@@ -665,6 +660,11 @@ fn Test(missing_less: Cpp.MissingLess,
 // CHECK:STDOUT:   %pattern_type.51d1c4.2: type = pattern_type %U [symbolic]
 // CHECK:STDOUT:   %y.param_patt.be3: %pattern_type.51d1c4.2 = value_param_pattern [symbolic]
 // CHECK:STDOUT:   %y.patt.b85: %pattern_type.51d1c4.2 = at_binding_pattern y, %y.param_patt.be3 [symbolic]
+// CHECK:STDOUT:   %OrderedWith.assoc_type.1d2e6f.2: type = assoc_entity_type @OrderedWith.1, @OrderedWith.1(%U) [symbolic]
+// CHECK:STDOUT:   %assoc0.c0023b.2: %OrderedWith.assoc_type.1d2e6f.2 = assoc_entity element0, imports.%Core.import_ref.e7a [symbolic]
+// CHECK:STDOUT:   %assoc1.3efd77.2: %OrderedWith.assoc_type.1d2e6f.2 = assoc_entity element1, imports.%Core.import_ref.3f7 [symbolic]
+// CHECK:STDOUT:   %assoc2.48eff0.2: %OrderedWith.assoc_type.1d2e6f.2 = assoc_entity element2, imports.%Core.import_ref.385 [symbolic]
+// CHECK:STDOUT:   %assoc3.5d53f7.2: %OrderedWith.assoc_type.1d2e6f.2 = assoc_entity element3, imports.%Core.import_ref.39b [symbolic]
 // CHECK:STDOUT:   %require_complete.3c0: <witness> = require_complete_type %OrderedWith.type.32ae87.2 [symbolic]
 // CHECK:STDOUT:   %assoc0.13c: %OrderedWith.assoc_type.1d2e6f.1 = assoc_entity element0, imports.%Core.import_ref.447 [symbolic]
 // CHECK:STDOUT:   %OrderedWith.lookup_impl_witness: <witness> = lookup_impl_witness %T, @OrderedWith.1, @OrderedWith.1(%U) [symbolic]
diff --git a/toolchain/check/testdata/interop/cpp/operators/spaceship.carbon b/toolchain/check/testdata/interop/cpp/operators/spaceship.carbon
index 229fcd4b64f4..1f66d9b0b188 100644
--- a/toolchain/check/testdata/interop/cpp/operators/spaceship.carbon
+++ b/toolchain/check/testdata/interop/cpp/operators/spaceship.carbon
@@ -244,9 +244,6 @@ fn Test(returns_strong_ordering: Cpp.ReturnsStrongOrdering) {
 // CHECK:STDOUT:   %pattern_type.3d4: type = pattern_type %EqWith.type.98ea86.2 [symbolic]
 // CHECK:STDOUT:   %T.patt.6b9: %pattern_type.3d4 = symbolic_binding_pattern T, 1 [symbolic]
 // CHECK:STDOUT:   %T.d94: %EqWith.type.98ea86.2 = symbolic_binding T, 1 [symbolic]
-// CHECK:STDOUT:   %EqWith.assoc_type.85b122.2: type = assoc_entity_type @EqWith.1, @EqWith.1(%U) [symbolic]
-// CHECK:STDOUT:   %assoc0.eee873.2: %EqWith.assoc_type.85b122.2 = assoc_entity element0, imports.%Core.import_ref.5ba [symbolic]
-// CHECK:STDOUT:   %assoc1.0ffc88.2: %EqWith.assoc_type.85b122.2 = assoc_entity element1, imports.%Core.import_ref.03f [symbolic]
 // CHECK:STDOUT:   %T.as_type.93d: type = facet_access_type %T.d94 [symbolic]
 // CHECK:STDOUT:   %pattern_type.e6374a.2: type = pattern_type %T.as_type.93d [symbolic]
 // CHECK:STDOUT:   %x.param_patt.aa2: %pattern_type.e6374a.2 = value_param_pattern [symbolic]
@@ -254,6 +251,9 @@ fn Test(returns_strong_ordering: Cpp.ReturnsStrongOrdering) {
 // CHECK:STDOUT:   %pattern_type.51d1c4.2: type = pattern_type %U [symbolic]
 // CHECK:STDOUT:   %y.param_patt.be3: %pattern_type.51d1c4.2 = value_param_pattern [symbolic]
 // CHECK:STDOUT:   %y.patt.b85: %pattern_type.51d1c4.2 = at_binding_pattern y, %y.param_patt.be3 [symbolic]
+// CHECK:STDOUT:   %EqWith.assoc_type.85b122.2: type = assoc_entity_type @EqWith.1, @EqWith.1(%U) [symbolic]
+// CHECK:STDOUT:   %assoc0.eee873.2: %EqWith.assoc_type.85b122.2 = assoc_entity element0, imports.%Core.import_ref.5ba [symbolic]
+// CHECK:STDOUT:   %assoc1.0ffc88.2: %EqWith.assoc_type.85b122.2 = assoc_entity element1, imports.%Core.import_ref.03f [symbolic]
 // CHECK:STDOUT:   %require_complete.fb5: <witness> = require_complete_type %EqWith.type.98ea86.2 [symbolic]
 // CHECK:STDOUT:   %assoc0.d00: %EqWith.assoc_type.85b122.1 = assoc_entity element0, imports.%Core.import_ref.2e5 [symbolic]
 // CHECK:STDOUT:   %EqWith.lookup_impl_witness: <witness> = lookup_impl_witness %T.d94, @EqWith.1, @EqWith.1(%U) [symbolic]
@@ -281,15 +281,15 @@ fn Test(returns_strong_ordering: Cpp.ReturnsStrongOrdering) {
 // CHECK:STDOUT:   %pattern_type.ebc: type = pattern_type %OrderedWith.type.32ae87.2 [symbolic]
 // CHECK:STDOUT:   %T.patt.aaa: %pattern_type.ebc = symbolic_binding_pattern T, 1 [symbolic]
 // CHECK:STDOUT:   %T.7df: %OrderedWith.type.32ae87.2 = symbolic_binding T, 1 [symbolic]
+// CHECK:STDOUT:   %T.as_type.262: type = facet_access_type %T.7df [symbolic]
+// CHECK:STDOUT:   %pattern_type.f6ec4f.2: type = pattern_type %T.as_type.262 [symbolic]
+// CHECK:STDOUT:   %x.param_patt.a58: %pattern_type.f6ec4f.2 = value_param_pattern [symbolic]
+// CHECK:STDOUT:   %x.patt.140: %pattern_type.f6ec4f.2 = at_binding_pattern x, %x.param_patt.a58 [symbolic]
 // CHECK:STDOUT:   %OrderedWith.assoc_type.1d2e6f.2: type = assoc_entity_type @OrderedWith.1, @OrderedWith.1(%U) [symbolic]
 // CHECK:STDOUT:   %assoc0.c0023b.2: %OrderedWith.assoc_type.1d2e6f.2 = assoc_entity element0, imports.%Core.import_ref.e7a [symbolic]
 // CHECK:STDOUT:   %assoc1.3efd77.2: %OrderedWith.assoc_type.1d2e6f.2 = assoc_entity element1, imports.%Core.import_ref.3f7 [symbolic]
 // CHECK:STDOUT:   %assoc2.48eff0.2: %OrderedWith.assoc_type.1d2e6f.2 = assoc_entity element2, imports.%Core.import_ref.385 [symbolic]
 // CHECK:STDOUT:   %assoc3.5d53f7.2: %OrderedWith.assoc_type.1d2e6f.2 = assoc_entity element3, imports.%Core.import_ref.39b [symbolic]
-// CHECK:STDOUT:   %T.as_type.262: type = facet_access_type %T.7df [symbolic]
-// CHECK:STDOUT:   %pattern_type.f6ec4f.2: type = pattern_type %T.as_type.262 [symbolic]
-// CHECK:STDOUT:   %x.param_patt.a58: %pattern_type.f6ec4f.2 = value_param_pattern [symbolic]
-// CHECK:STDOUT:   %x.patt.140: %pattern_type.f6ec4f.2 = at_binding_pattern x, %x.param_patt.a58 [symbolic]
 // CHECK:STDOUT:   %require_complete.3c0: <witness> = require_complete_type %OrderedWith.type.32ae87.2 [symbolic]
 // CHECK:STDOUT:   %assoc0.13c: %OrderedWith.assoc_type.1d2e6f.1 = assoc_entity element0, imports.%Core.import_ref.447 [symbolic]
 // CHECK:STDOUT:   %OrderedWith.lookup_impl_witness: <witness> = lookup_impl_witness %T.7df, @OrderedWith.1, @OrderedWith.1(%U) [symbolic]
diff --git a/toolchain/check/testdata/named_constraint/empty_generic.carbon b/toolchain/check/testdata/named_constraint/empty_generic.carbon
index 0858f50ae26c..880e708f09ff 100644
--- a/toolchain/check/testdata/named_constraint/empty_generic.carbon
+++ b/toolchain/check/testdata/named_constraint/empty_generic.carbon
@@ -39,7 +39,7 @@ fn G(generic T: Z, generic U: Empty(T), generic V: type) {
 // CHECK:STDOUT:   %empty_tuple.type: type = tuple_type () [concrete]
 // CHECK:STDOUT:   %empty_struct.26b: %Empty.type.f30 = struct_value () [concrete]
 // CHECK:STDOUT:   %Empty.type.d682d6.1: type = facet_type <@Empty, @Empty(%T.67d)> [symbolic]
-// CHECK:STDOUT:   %Self.22bbf7.1: %Empty.type.d682d6.1 = symbolic_binding Self, 1 [symbolic]
+// CHECK:STDOUT:   %Self.22b: %Empty.type.d682d6.1 = symbolic_binding Self, 1 [symbolic]
 // CHECK:STDOUT:   %pattern_type.9a587c.1: type = pattern_type %Empty.type.d682d6.1 [symbolic]
 // CHECK:STDOUT:   %U.patt.cb839c.1: %pattern_type.9a587c.1 = symbolic_binding_pattern U, 1 [symbolic]
 // CHECK:STDOUT:   %U.e1f642.1: %Empty.type.d682d6.1 = symbolic_binding U, 1 [symbolic]
@@ -68,7 +68,6 @@ fn G(generic T: Z, generic U: Empty(T), generic V: type) {
 // CHECK:STDOUT:   %F.specific_fn.d75: <specific function> = specific_function %F, @F(%T.as_type, %Empty.facet.2cb) [symbolic]
 // CHECK:STDOUT:   %Empty.facet.aa1: %Empty.type.d682d6.2 = facet_value %T.as_type, () [symbolic]
 // CHECK:STDOUT:   %F.specific_fn.7a2: <specific function> = specific_function %F, @F(%T.as_type, %Empty.facet.aa1) [symbolic]
-// CHECK:STDOUT:   %Self.22bbf7.2: %Empty.type.d682d6.2 = symbolic_binding Self, 1 [symbolic]
 // CHECK:STDOUT:   %F.specific_fn.ff9: <specific function> = specific_function %F, @F(%T.as_type, %U.e1f642.2) [symbolic]
 // CHECK:STDOUT:   %facet_value.ed5: %type = facet_value %V, () [symbolic]
 // CHECK:STDOUT:   %Empty.facet.ed5: %Empty.type.d682d6.2 = facet_value %V, () [symbolic]
@@ -135,10 +134,10 @@ fn G(generic T: Z, generic U: Empty(T), generic V: type) {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !definition:
 // CHECK:STDOUT:   %Empty.type: type = facet_type <@Empty, @Empty(%T.loc16_19.1)> [symbolic = %Empty.type (constants.%Empty.type.d682d6.1)]
-// CHECK:STDOUT:   %Self.loc16_27.2: @Empty.%Empty.type (%Empty.type.d682d6.1) = symbolic_binding Self, 1 [symbolic = %Self.loc16_27.2 (constants.%Self.22bbf7.1)]
+// CHECK:STDOUT:   %Self.loc16_27.2: @Empty.%Empty.type (%Empty.type.d682d6.1) = symbolic_binding Self, 1 [symbolic = %Self.loc16_27.2 (constants.%Self.22b)]
 // CHECK:STDOUT:
 // CHECK:STDOUT:   constraint {
-// CHECK:STDOUT:     %Self.loc16_27.1: @Empty.%Empty.type (%Empty.type.d682d6.1) = symbolic_binding Self, 1 [symbolic = %Self.loc16_27.2 (constants.%Self.22bbf7.1)]
+// CHECK:STDOUT:     %Self.loc16_27.1: @Empty.%Empty.type (%Empty.type.d682d6.1) = symbolic_binding Self, 1 [symbolic = %Self.loc16_27.2 (constants.%Self.22b)]
 // CHECK:STDOUT:     %Empty.WithSelf.decl = constraint_with_self_decl @Empty [concrete]
 // CHECK:STDOUT:
 // CHECK:STDOUT:   !members:
@@ -243,7 +242,7 @@ fn G(generic T: Z, generic U: Empty(T), generic V: type) {
 // CHECK:STDOUT:   %T.loc16_19.1 => constants.%T.67d
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific @Empty.WithSelf(constants.%T.67d, constants.%Self.22bbf7.1) {}
+// CHECK:STDOUT: specific @Empty.WithSelf(constants.%T.67d, constants.%Self.22b) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: specific @F(constants.%T.67d, constants.%U.e1f642.1) {
 // CHECK:STDOUT:   %T.patt.loc18_15.2 => constants.%T.patt.d47
@@ -257,10 +256,6 @@ fn G(generic T: Z, generic U: Empty(T), generic V: type) {
 // CHECK:STDOUT: specific @Empty(constants.%T.as_type) {
 // CHECK:STDOUT:   %T.patt.loc16_19.2 => constants.%T.patt.d47
 // CHECK:STDOUT:   %T.loc16_19.1 => constants.%T.as_type
-// CHECK:STDOUT:
-// CHECK:STDOUT: !definition:
-// CHECK:STDOUT:   %Empty.type => constants.%Empty.type.d682d6.2
-// CHECK:STDOUT:   %Self.loc16_27.2 => constants.%Self.22bbf7.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: specific @G(constants.%T.013, constants.%U.e1f642.2, constants.%V) {
@@ -320,10 +315,6 @@ fn G(generic T: Z, generic U: Empty(T), generic V: type) {
 // CHECK:STDOUT: !definition:
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific @Empty.WithSelf(constants.%T.as_type, constants.%Self.22bbf7.1) {
-// CHECK:STDOUT: !definition:
-// CHECK:STDOUT: }
-// CHECK:STDOUT:
 // CHECK:STDOUT: specific @F(constants.%T.as_type, constants.%U.e1f642.2) {
 // CHECK:STDOUT:   %T.patt.loc18_15.2 => constants.%T.patt.d47
 // CHECK:STDOUT:   %T.loc18_15.1 => constants.%T.as_type
diff --git a/toolchain/check/testdata/named_constraint/require.carbon b/toolchain/check/testdata/named_constraint/require.carbon
index 7879f99238b9..522151d86084 100644
--- a/toolchain/check/testdata/named_constraint/require.carbon
+++ b/toolchain/check/testdata/named_constraint/require.carbon
@@ -1084,9 +1084,7 @@ constraint N {
 // CHECK:STDOUT:   %Self.as_type.loc9_11.2: type = facet_access_type %Self [symbolic = %Self.as_type.loc9_11.2 (constants.%Self.as_type)]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific @Z.WithSelf(constants.%Self.d87) {
-// CHECK:STDOUT: !definition:
-// CHECK:STDOUT: }
+// CHECK:STDOUT: specific @Z.WithSelf(constants.%Self.d87) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: specific @Z.WithSelf.Self.as_type.impls.Y.type.require(constants.%Self.d87) {
 // CHECK:STDOUT:   %Self => constants.%Self.d87
@@ -1147,9 +1145,7 @@ constraint N {
 // CHECK:STDOUT:   %Self.as_type.loc9_11.2: type = facet_access_type %Self [symbolic = %Self.as_type.loc9_11.2 (constants.%Self.as_type)]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific @Z.WithSelf(constants.%Self.d87) {
-// CHECK:STDOUT: !definition:
-// CHECK:STDOUT: }
+// CHECK:STDOUT: specific @Z.WithSelf(constants.%Self.d87) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: specific @Z.WithSelf.Self.as_type.impls.Y.type.require(constants.%Self.d87) {
 // CHECK:STDOUT:   %Self => constants.%Self.d87
@@ -1542,9 +1538,7 @@ constraint N {
 // CHECK:STDOUT:   %Z_where.type.loc10_19.3: type = facet_type <@Z where .Self impls @Y, @Y(%Self.as_type.loc10_11.2)> [symbolic = %Z_where.type.loc10_19.3 (constants.%Z_where.type.0d5)]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific @N.WithSelf(constants.%Self.d87) {
-// CHECK:STDOUT: !definition:
-// CHECK:STDOUT: }
+// CHECK:STDOUT: specific @N.WithSelf(constants.%Self.d87) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: specific @N.WithSelf.Self.as_type.impls.Z_where.type.require(constants.%Self.d87) {
 // CHECK:STDOUT:   %Self => constants.%Self.d87
@@ -1650,9 +1644,7 @@ constraint N {
 // CHECK:STDOUT:   %Z_where.type.loc10_19.3: type = facet_type <@Z where %C.loc10_19 impls @Y, @Y(%Self.as_type.loc10_11.2)> [symbolic = %Z_where.type.loc10_19.3 (constants.%Z_where.type.a0f3c6.2)]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: specific @N.WithSelf(constants.%Self.d87) {
-// CHECK:STDOUT: !definition:
-// CHECK:STDOUT: }
+// CHECK:STDOUT: specific @N.WithSelf(constants.%Self.d87) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: specific @N.WithSelf.Self.as_type.impls.Z_where.type.require(constants.%Self.d87) {
 // CHECK:STDOUT:   %Self => constants.%Self.d87
diff --git a/toolchain/check/type_completion.cpp b/toolchain/check/type_completion.cpp
index f066ebabd7ae..991b38c4e4a9 100644
--- a/toolchain/check/type_completion.cpp
+++ b/toolchain/check/type_completion.cpp
@@ -438,6 +438,9 @@ auto TypeCompleter::ProcessStep() -> bool {
 }
 
 auto TypeCompleter::AddNestedIncompleteTypes(SemIR::Inst type_inst) -> bool {
+  // NOTE: `TryToCompleteClassType()` in convert.cpp matches the same types as
+  // the switch here. When adding a new type here, it should also be added
+  // there.
   CARBON_KIND_SWITCH(type_inst) {
     case CARBON_KIND(SemIR::ArrayType inst): {
       Push(context_->types().GetTypeIdForTypeInstId(inst.element_type_inst_id));