diff --git a/toolchain/check/impl_lookup.cpp b/toolchain/check/impl_lookup.cpp
index f04019faa26e..549e8d0a91e7 100644
--- a/toolchain/check/impl_lookup.cpp
+++ b/toolchain/check/impl_lookup.cpp
@@ -173,16 +173,15 @@ static auto GetInterfacesFromConstantId(
   const auto& facet_type_info =
       context.facet_types().Get(facet_type_inst.facet_type_id);
   has_other_requirements = facet_type_info.other_requirements;
-  // TODO: Once we add support for named constraints, we will need to change
-  // this to return the same interfaces as in the complete facet type.
+  // TODO: This needs to match the order of witnesses for the facet type, which
+  // will need to be maintained once we add support for named constraints.
   return facet_type_info.impls_constraints;
 }
 
-static auto GetWitnessIdForImpl(
-    Context& context, SemIR::LocId loc_id,
-    SemIR::ConstantId query_self_const_id,
-    const SemIR::CompleteFacetType::RequiredInterface& interface,
-    SemIR::ImplId impl_id) -> SemIR::InstId {
+static auto GetWitnessIdForImpl(Context& context, SemIR::LocId loc_id,
+                                SemIR::ConstantId query_self_const_id,
+                                const SemIR::SpecificInterface& interface,
+                                SemIR::ImplId impl_id) -> SemIR::InstId {
   // The impl may have generic arguments, in which case we need to deduce them
   // to find what they are given the specific type and interface query. We use
   // that specific to map values in the impl to the deduced values.
@@ -275,26 +274,22 @@ static auto FindWitnessInFacet(
   SemIR::TypeId facet_type_id = context.insts().Get(facet_inst_id).type_id();
   if (auto facet_type_inst =
           context.types().TryGetAs<SemIR::FacetType>(facet_type_id)) {
-    auto complete_facet_type_id = RequireCompleteFacetType(
-        context, facet_type_id, loc_id, *facet_type_inst,
-        [&]() -> DiagnosticBuilder {
-          context.TODO(loc_id, "impl lookup on incomplete facet type");
-          return context.emitter().BuildSuppressed();
-        });
-    if (complete_facet_type_id.has_value()) {
-      const auto& complete_facet_type =
-          context.complete_facet_types().Get(complete_facet_type_id);
-      for (auto [index, interface] :
-           llvm::enumerate(complete_facet_type.required_interfaces)) {
-        if (interface == specific_interface) {
-          return GetOrAddInst(
-              context, loc_id,
-              SemIR::FacetAccessWitness{
-                  .type_id = GetSingletonType(
-                      context, SemIR::WitnessType::SingletonInstId),
-                  .facet_value_inst_id = facet_inst_id,
-                  .index = SemIR::ElementIndex(index)});
-        }
+    const auto& facet_type_info =
+        context.facet_types().Get(facet_type_inst->facet_type_id);
+    // TODO: This depends on the index into `impls_constraints` matching
+    // the index into the facet type witness. This will have to be maintained
+    // even for facet types that include named constraints, once that is
+    // supported.
+    for (auto [index, interface] :
+         llvm::enumerate(facet_type_info.impls_constraints)) {
+      if (interface == specific_interface) {
+        return GetOrAddInst(
+            context, loc_id,
+            SemIR::FacetAccessWitness{
+                .type_id = GetSingletonType(
+                    context, SemIR::WitnessType::SingletonInstId),
+                .facet_value_inst_id = facet_inst_id,
+                .index = SemIR::ElementIndex(index)});
       }
     }
   }
@@ -415,9 +410,9 @@ auto LookupImplWitness(Context& context, SemIR::LocId loc_id,
       .query_self_const_id = query_self_const_id,
       .query_facet_type_const_id = query_facet_type_const_id,
   });
-  // We need to find a witness for each interface in `interfaces`. We return
-  // them in the same order as they are found in the `CompleteFacetType`, which
-  // is the same order as in `interfaces` here.
+  // We need to find a witness for each interface in `interfaces`. Every
+  // consumer of a facet type needs to agree on the order of interfaces used for
+  // its witnesses.
   for (const auto& interface : interfaces) {
     // TODO: Since both `interfaces` and `query_self_const_id` are sorted lists,
     // do an O(N+M) merge instead of O(N*M) nested loops.
diff --git a/toolchain/check/testdata/interface/no_prelude/fail_assoc_const_alias.carbon b/toolchain/check/testdata/interface/no_prelude/fail_assoc_const_alias.carbon
index 6e715aaf9fd2..051adb980421 100644
--- a/toolchain/check/testdata/interface/no_prelude/fail_assoc_const_alias.carbon
+++ b/toolchain/check/testdata/interface/no_prelude/fail_assoc_const_alias.carbon
@@ -26,10 +26,6 @@ interface I {
 
 interface J {
   alias U = I.T;
-  // CHECK:STDERR: fail_alias_to_different_interface.carbon:[[@LINE+11]]:13: error: semantics TODO: `impl lookup on incomplete facet type` [SemanticsTodo]
-  // CHECK:STDERR:   fn F() -> U;
-  // CHECK:STDERR:             ^
-  // CHECK:STDERR:
   // CHECK:STDERR: fail_alias_to_different_interface.carbon:[[@LINE+7]]:13: error: cannot implicitly convert type `Self` that implements `J` into type implementing `I` [ConversionFailureFacetToFacet]
   // CHECK:STDERR:   fn F() -> U;
   // CHECK:STDERR:             ^
@@ -55,10 +51,6 @@ impl forall [V:! J2] V as I2 where .T2 = () {}
 
 interface J2 {
   alias U2 = I2.T2;
-  // CHECK:STDERR: fail_todo_alias_to_different_interface_with_requires.carbon:[[@LINE+11]]:14: error: semantics TODO: `impl lookup on incomplete facet type` [SemanticsTodo]
-  // CHECK:STDERR:   fn F2() -> U2;
-  // CHECK:STDERR:              ^~
-  // CHECK:STDERR:
   // CHECK:STDERR: fail_todo_alias_to_different_interface_with_requires.carbon:[[@LINE+7]]:14: error: cannot implicitly convert type `Self` that implements `J2` into type implementing `I2` [ConversionFailureFacetToFacet]
   // CHECK:STDERR:   fn F2() -> U2;
   // CHECK:STDERR:              ^~
@@ -277,7 +269,7 @@ interface C {
 // CHECK:STDOUT:     %return.patt: <error> = return_slot_pattern
 // CHECK:STDOUT:     %return.param_patt: <error> = out_param_pattern %return.patt, call_param0
 // CHECK:STDOUT:   } {
-// CHECK:STDOUT:     %.loc22: %I.type = converted @J.%Self, <error> [concrete = <error>]
+// CHECK:STDOUT:     %.loc18: %I.type = converted @J.%Self, <error> [concrete = <error>]
 // CHECK:STDOUT:     %U.ref: <error> = name_ref U, <error> [concrete = <error>]
 // CHECK:STDOUT:     %return.param: ref <error> = out_param call_param0
 // CHECK:STDOUT:     %return: ref <error> = return_slot %return.param
@@ -475,10 +467,10 @@ interface C {
 // CHECK:STDOUT:     %return.patt: <error> = return_slot_pattern
 // CHECK:STDOUT:     %return.param_patt: <error> = out_param_pattern %return.patt, call_param0
 // CHECK:STDOUT:   } {
-// CHECK:STDOUT:     %Self.as_type.loc26_14.2: type = facet_access_type constants.%Self.541 [symbolic = %Self.as_type.loc26_14.1 (constants.%Self.as_type.f5c)]
-// CHECK:STDOUT:     %.loc26_14.1: type = converted constants.%Self.541, %Self.as_type.loc26_14.2 [symbolic = %Self.as_type.loc26_14.1 (constants.%Self.as_type.f5c)]
-// CHECK:STDOUT:     %.loc26_14.2: %J2.type = converted %.loc26_14.1, constants.%Self.541 [symbolic = %Self (constants.%Self.541)]
-// CHECK:STDOUT:     %.loc26_14.3: %I2.type = converted @J2.%Self, <error> [concrete = <error>]
+// CHECK:STDOUT:     %Self.as_type.loc22_14.2: type = facet_access_type constants.%Self.541 [symbolic = %Self.as_type.loc22_14.1 (constants.%Self.as_type.f5c)]
+// CHECK:STDOUT:     %.loc22_14.1: type = converted constants.%Self.541, %Self.as_type.loc22_14.2 [symbolic = %Self.as_type.loc22_14.1 (constants.%Self.as_type.f5c)]
+// CHECK:STDOUT:     %.loc22_14.2: %J2.type = converted %.loc22_14.1, constants.%Self.541 [symbolic = %Self (constants.%Self.541)]
+// CHECK:STDOUT:     %.loc22_14.3: %I2.type = converted @J2.%Self, <error> [concrete = <error>]
 // CHECK:STDOUT:     %U2.ref: <error> = name_ref U2, <error> [concrete = <error>]
 // CHECK:STDOUT:     %return.param: ref <error> = out_param call_param0
 // CHECK:STDOUT:     %return: ref <error> = return_slot %return.param
@@ -542,7 +534,7 @@ interface C {
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic fn @F2(@J2.%Self: %J2.type) {
 // CHECK:STDOUT:   %Self: %J2.type = bind_symbolic_name Self, 0 [symbolic = %Self (constants.%Self.541)]
-// CHECK:STDOUT:   %Self.as_type.loc26_14.1: type = facet_access_type %Self [symbolic = %Self.as_type.loc26_14.1 (constants.%Self.as_type.f5c)]
+// CHECK:STDOUT:   %Self.as_type.loc22_14.1: type = facet_access_type %Self [symbolic = %Self.as_type.loc22_14.1 (constants.%Self.as_type.f5c)]
 // CHECK:STDOUT:
 // CHECK:STDOUT:   fn() -> <error>;
 // CHECK:STDOUT: }
@@ -598,7 +590,7 @@ interface C {
 // CHECK:STDOUT:
 // CHECK:STDOUT: specific @F2(constants.%Self.541) {
 // CHECK:STDOUT:   %Self => constants.%Self.541
-// CHECK:STDOUT:   %Self.as_type.loc26_14.1 => constants.%Self.as_type.f5c
+// CHECK:STDOUT:   %Self.as_type.loc22_14.1 => constants.%Self.as_type.f5c
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- fail_call_method_alias.carbon
diff --git a/toolchain/check/testdata/interface/no_prelude/generic.carbon b/toolchain/check/testdata/interface/no_prelude/generic.carbon
index 64a7fb81dbb7..32b2f15b8f02 100644
--- a/toolchain/check/testdata/interface/no_prelude/generic.carbon
+++ b/toolchain/check/testdata/interface/no_prelude/generic.carbon
@@ -510,10 +510,6 @@ fn G(T:! Generic(B)) {
 // CHECK:STDOUT: specific @Generic(constants.%B) {
 // CHECK:STDOUT:   %T.loc4_19.2 => constants.%B
 // CHECK:STDOUT:   %T.patt.loc4_19.2 => constants.%B
-// CHECK:STDOUT:
-// CHECK:STDOUT: !definition:
-// CHECK:STDOUT:   %Generic.type => constants.%Generic.type.4ce
-// CHECK:STDOUT:   %Self.2 => constants.%Self
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: specific @G(constants.%T.bae) {