diff --git a/toolchain/check/eval.cpp b/toolchain/check/eval.cpp
index f7a9af84a368..09f19906d0e2 100644
--- a/toolchain/check/eval.cpp
+++ b/toolchain/check/eval.cpp
@@ -250,9 +250,8 @@ enum class Phase : uint8_t {
 };
 }  // namespace
 
-// Returns whether the specified phase is a constant phase.
-static auto IsConstant(Phase phase) -> bool {
-  return phase < Phase::UnknownDueToError;
+static auto IsConstantOrError(Phase phase) -> bool {
+  return phase != Phase::Runtime;
 }
 
 // Gets the phase in which the value of a constant will become available.
@@ -700,7 +699,7 @@ static auto ReplaceFieldWithConstantValue(EvalContext& eval_context,
     return false;
   }
   inst->*field = unwrapped;
-  return true;
+  return IsConstantOrError(*phase);
 }
 
 // Function template that can be called with an argument of type `T`. Used below
@@ -765,13 +764,12 @@ static auto ReplaceAllFieldsWithConstantValues(EvalContext& eval_context,
     -> bool {
   auto arg0 =
       GetConstantValueForArg(eval_context, inst->arg0_and_kind(), phase);
-  if (!IsConstant(*phase)) {
+  if (!IsConstantOrError(*phase)) {
     return false;
   }
-
   auto arg1 =
       GetConstantValueForArg(eval_context, inst->arg1_and_kind(), phase);
-  if (!IsConstant(*phase)) {
+  if (!IsConstantOrError(*phase)) {
     return false;
   }
   inst->SetArgs(arg0, arg1);
@@ -786,7 +784,7 @@ static auto ReplaceTypeWithConstantValue(EvalContext& eval_context,
                                          SemIR::Inst* inst, Phase* phase)
     -> bool {
   inst->SetType(GetTypeOfInst(eval_context, inst_id, *inst, phase));
-  return IsConstant(*phase);
+  return IsConstantOrError(*phase);
 }
 
 template <typename InstT>
@@ -794,7 +792,7 @@ static auto ReplaceTypeWithConstantValue(EvalContext& eval_context,
                                          SemIR::InstId inst_id, InstT* inst,
                                          Phase* phase) -> bool {
   inst->type_id = GetTypeOfInst(eval_context, inst_id, *inst, phase);
-  return IsConstant(*phase);
+  return IsConstantOrError(*phase);
 }
 
 template <typename... Types>
@@ -1835,7 +1833,7 @@ static auto ComputeInstPhase(Context& context, SemIR::Inst inst) -> Phase {
                         context.types().GetConstantId(inst.type_id()));
   GetConstantValueForArg(eval_context, inst.arg0_and_kind(), &phase);
   GetConstantValueForArg(eval_context, inst.arg1_and_kind(), &phase);
-  CARBON_CHECK(phase != Phase::Runtime);
+  CARBON_CHECK(IsConstantOrError(phase));
   return phase;
 }
 
@@ -1890,10 +1888,14 @@ static auto TryEvalTypedInst(EvalContext& eval_context, SemIR::InstId inst_id,
     if (!ReplaceTypeWithConstantValue(eval_context, inst_id, &inst, &phase) ||
         !ReplaceAllFieldsWithConstantValues(eval_context, &inst, &phase)) {
       if constexpr (ConstantKind == SemIR::InstConstantKind::Always) {
-        CARBON_CHECK(phase == Phase::UnknownDueToError,
-                     "{0} should always be constant", InstT::Kind);
+        CARBON_FATAL("{0} should always be constant", InstT::Kind);
       }
-      return MakeNonConstantResult(phase);
+      return SemIR::ConstantId::NotConstant;
+    }
+    // If any operand of the instruction has an error in it, the instruction
+    // itself evaluates to an error.
+    if (phase == Phase::UnknownDueToError) {
+      return SemIR::ErrorInst::ConstantId;
     }
 
     // When canonicalizing a SpecificId, we defer resolving the specific's
@@ -1993,8 +1995,9 @@ auto TryEvalTypedInst<SemIR::BindSymbolicName>(EvalContext& eval_context,
       !ReplaceFieldWithConstantValue(eval_context, &bind,
                                      &SemIR::BindSymbolicName::entity_name_id,
                                      &phase)) {
-    return MakeNonConstantResult(phase);
+    return SemIR::ConstantId::NotConstant;
   }
+  // This correctly handles `Phase::UnknownDueToError`.
   return MakeConstantResult(eval_context.context(), bind, phase);
 }
 
diff --git a/toolchain/check/testdata/class/import_access.carbon b/toolchain/check/testdata/class/import_access.carbon
index 328882dcb609..ee47ef6aa791 100644
--- a/toolchain/check/testdata/class/import_access.carbon
+++ b/toolchain/check/testdata/class/import_access.carbon
@@ -505,7 +505,7 @@ private class Redecl {}
 // CHECK:STDOUT:       %Forward.ref: <error> = name_ref Forward, <error> [concrete = <error>]
 // CHECK:STDOUT:       %ptr: type = ptr_type <error> [concrete = <error>]
 // CHECK:STDOUT:     }
-// CHECK:STDOUT:     %c: <error> = bind_name c, %c.param [concrete = <error>]
+// CHECK:STDOUT:     %c: <error> = bind_name c, %c.param
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -544,7 +544,7 @@ private class Redecl {}
 // CHECK:STDOUT:       %Forward.ref: <error> = name_ref Forward, <error> [concrete = <error>]
 // CHECK:STDOUT:       %ptr: type = ptr_type <error> [concrete = <error>]
 // CHECK:STDOUT:     }
-// CHECK:STDOUT:     %c: <error> = bind_name c, %c.param [concrete = <error>]
+// CHECK:STDOUT:     %c: <error> = bind_name c, %c.param
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/deduce/int_float.carbon b/toolchain/check/testdata/deduce/int_float.carbon
index e0c39b2062f4..3d7398952e79 100644
--- a/toolchain/check/testdata/deduce/int_float.carbon
+++ b/toolchain/check/testdata/deduce/int_float.carbon
@@ -241,7 +241,7 @@ fn G(a: f64) -> Core.IntLiteral() {
 // CHECK:STDOUT:       %.loc9_44.1: type = value_of_initializer %float.make_type
 // CHECK:STDOUT:       %.loc9_44.2: type = converted %float.make_type, %.loc9_44.1
 // CHECK:STDOUT:     }
-// CHECK:STDOUT:     %n: <error> = bind_name n, %n.param [concrete = <error>]
+// CHECK:STDOUT:     %n: <error> = bind_name n, %n.param
 // CHECK:STDOUT:     %return.param: ref Core.IntLiteral = out_param call_param1
 // CHECK:STDOUT:     %return: ref Core.IntLiteral = return_slot %return.param
 // CHECK:STDOUT:   }
diff --git a/toolchain/check/testdata/deduce/value_with_type_through_access.carbon b/toolchain/check/testdata/deduce/value_with_type_through_access.carbon
index a58a398b83da..7057f02d89af 100644
--- a/toolchain/check/testdata/deduce/value_with_type_through_access.carbon
+++ b/toolchain/check/testdata/deduce/value_with_type_through_access.carbon
@@ -636,7 +636,7 @@ fn G() {
 // CHECK:STDOUT:       %.loc21_38.1: ref type = class_element_access %T.ref.loc21_37, element0 [symbolic = %.loc21_38.3 (constants.%.2fe)]
 // CHECK:STDOUT:       %.loc21_38.2: type = bind_value %.loc21_38.1
 // CHECK:STDOUT:     }
-// CHECK:STDOUT:     %a: <error> = bind_name a, %a.param [concrete = <error>]
+// CHECK:STDOUT:     %a: <error> = bind_name a, %a.param
 // CHECK:STDOUT:   }
 // CHECK:STDOUT:   %C.decl: type = class_decl @C [concrete = constants.%C] {} {}
 // CHECK:STDOUT:   %G.decl: %G.type = fn_decl @G [concrete = constants.%G] {} {}
@@ -881,7 +881,7 @@ fn G() {
 // CHECK:STDOUT:       %.loc12_49.2: ref type = array_index %.loc12_49.1, %.loc12_48.2
 // CHECK:STDOUT:       %.loc12_49.3: type = bind_value %.loc12_49.2
 // CHECK:STDOUT:     }
-// CHECK:STDOUT:     %a: <error> = bind_name a, %a.param [concrete = <error>]
+// CHECK:STDOUT:     %a: <error> = bind_name a, %a.param
 // CHECK:STDOUT:   }
 // CHECK:STDOUT:   %C.decl: type = class_decl @C [concrete = constants.%C] {} {}
 // CHECK:STDOUT:   %G.decl: %G.type = fn_decl @G [concrete = constants.%G] {} {}
diff --git a/toolchain/check/testdata/facet/fail_deduction_uses_runtime_type_conversion.carbon b/toolchain/check/testdata/facet/fail_deduction_uses_runtime_type_conversion.carbon
index 6a88e6fb1c17..8ce33bc2ac83 100644
--- a/toolchain/check/testdata/facet/fail_deduction_uses_runtime_type_conversion.carbon
+++ b/toolchain/check/testdata/facet/fail_deduction_uses_runtime_type_conversion.carbon
@@ -293,7 +293,7 @@ fn G(holds_to: HoldsType((RuntimeConvertTo, ))) {
 // CHECK:STDOUT:   %.loc41_19.3: ref %RuntimeConvertTo = temporary %.loc41_19.1, %.loc41_19.2
 // CHECK:STDOUT:   %.loc41_19.4: %RuntimeConvertTo = bind_value %.loc41_19.3
 // CHECK:STDOUT:   %F.specific_fn: <specific function> = specific_function %F.ref, @F(constants.%tuple, <error>) [concrete = <error>]
-// CHECK:STDOUT:   %F.call: init %empty_tuple.type = call %F.specific_fn(%holds_to.ref) [concrete = <error>]
+// CHECK:STDOUT:   %F.call: init %empty_tuple.type = call %F.specific_fn(%holds_to.ref)
 // CHECK:STDOUT:   %impl.elem0.loc41_19.2: %.79d = impl_witness_access constants.%Destroy.impl_witness.3c9, element0 [concrete = constants.%Op.d2d]
 // CHECK:STDOUT:   %bound_method.loc41_19.2: <bound method> = bound_method %.loc41_19.1, %impl.elem0.loc41_19.2
 // CHECK:STDOUT:   %specific_fn.loc41: <specific function> = specific_function %impl.elem0.loc41_19.2, @Op.2(constants.%RuntimeConvertTo) [concrete = constants.%Op.specific_fn.373]
diff --git a/toolchain/check/testdata/function/declaration/fail_param_in_type.carbon b/toolchain/check/testdata/function/declaration/fail_param_in_type.carbon
index f75b21eb0fea..0bf26b8de4db 100644
--- a/toolchain/check/testdata/function/declaration/fail_param_in_type.carbon
+++ b/toolchain/check/testdata/function/declaration/fail_param_in_type.carbon
@@ -64,7 +64,7 @@ fn F(n: i32, a: array(i32, n)*);
 // CHECK:STDOUT:       %n.ref: %i32 = name_ref n, %n
 // CHECK:STDOUT:       %ptr: type = ptr_type <error> [concrete = <error>]
 // CHECK:STDOUT:     }
-// CHECK:STDOUT:     %a: <error> = bind_name a, %a.param [concrete = <error>]
+// CHECK:STDOUT:     %a: <error> = bind_name a, %a.param
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/function/definition/fail_decl_param_mismatch.carbon b/toolchain/check/testdata/function/definition/fail_decl_param_mismatch.carbon
index d22d728c0140..2f8e92102982 100644
--- a/toolchain/check/testdata/function/definition/fail_decl_param_mismatch.carbon
+++ b/toolchain/check/testdata/function/definition/fail_decl_param_mismatch.carbon
@@ -153,7 +153,7 @@ fn K() -> {} { return {}; }
 // CHECK:STDOUT:     %x.param_patt: <error> = value_param_pattern %x.patt, call_param0 [concrete]
 // CHECK:STDOUT:   } {
 // CHECK:STDOUT:     %x.param: <error> = value_param call_param0
-// CHECK:STDOUT:     %x: <error> = bind_name x, %x.param [concrete = <error>]
+// CHECK:STDOUT:     %x: <error> = bind_name x, %x.param
 // CHECK:STDOUT:   }
 // CHECK:STDOUT:   %I.decl.loc42: %I.type.af49c4.1 = fn_decl @I.1 [concrete = constants.%I.58e4ec.1] {} {}
 // CHECK:STDOUT:   %I.decl.loc50: %I.type.af49c4.2 = fn_decl @I.2 [concrete = constants.%I.58e4ec.2] {
diff --git a/toolchain/check/testdata/impl/fail_call_invalid.carbon b/toolchain/check/testdata/impl/fail_call_invalid.carbon
index ca9c78cd0e74..4020b4f930e2 100644
--- a/toolchain/check/testdata/impl/fail_call_invalid.carbon
+++ b/toolchain/check/testdata/impl/fail_call_invalid.carbon
@@ -123,7 +123,7 @@ fn InstanceCall(n: i32) {
 // CHECK:STDOUT:   } {
 // CHECK:STDOUT:     %self.param: <error> = value_param call_param0
 // CHECK:STDOUT:     %Undeclared.ref: <error> = name_ref Undeclared, <error> [concrete = <error>]
-// CHECK:STDOUT:     %self: <error> = bind_name self, %self.param [concrete = <error>]
+// CHECK:STDOUT:     %self: <error> = bind_name self, %self.param
 // CHECK:STDOUT:   }
 // CHECK:STDOUT:   %G.decl.loc24_27.2: %G.type.c9825d.2 = fn_decl @G.3 [concrete = constants.%G.e73e91.2] {
 // CHECK:STDOUT:     %self.patt: %pattern_type.7ce = binding_pattern self [concrete]
diff --git a/toolchain/check/testdata/impl/use_assoc_const.carbon b/toolchain/check/testdata/impl/use_assoc_const.carbon
index bc1115d06620..c52e5c328349 100644
--- a/toolchain/check/testdata/impl/use_assoc_const.carbon
+++ b/toolchain/check/testdata/impl/use_assoc_const.carbon
@@ -2370,7 +2370,7 @@ fn F() {
 // CHECK:STDOUT:       %U.ref.loc24_13: %J.assoc_type = name_ref U, @U.%assoc0 [concrete = constants.%assoc0.411]
 // CHECK:STDOUT:       %.loc24_13: type = converted %U.ref.loc24_13, <error> [concrete = <error>]
 // CHECK:STDOUT:     }
-// CHECK:STDOUT:     %u: <error> = bind_name u, %u.param [concrete = <error>]
+// CHECK:STDOUT:     %u: <error> = bind_name u, %u.param
 // CHECK:STDOUT:     %return.param: ref <error> = out_param call_param1
 // CHECK:STDOUT:     %return: ref <error> = return_slot %return.param
 // CHECK:STDOUT:   }
@@ -2433,7 +2433,7 @@ fn F() {
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F.2(%u.param: <error>) -> <error> {
 // CHECK:STDOUT: !entry:
-// CHECK:STDOUT:   %u.ref: <error> = name_ref u, %u [concrete = <error>]
+// CHECK:STDOUT:   %u.ref: <error> = name_ref u, %u
 // CHECK:STDOUT:   return <error>
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -2583,7 +2583,7 @@ fn F() {
 // CHECK:STDOUT:     %self: @F.1.%Self.as_type.loc19_14.1 (%Self.as_type) = bind_name self, %self.param
 // CHECK:STDOUT:     %z.param: <error> = value_param call_param1
 // CHECK:STDOUT:     %Self.ref.loc19_23: %J2.type = name_ref Self, @J2.%Self [symbolic = %Self (constants.%Self)]
-// CHECK:STDOUT:     %z: <error> = bind_name z, %z.param [concrete = <error>]
+// CHECK:STDOUT:     %z: <error> = bind_name z, %z.param
 // CHECK:STDOUT:     %return.param: ref <error> = out_param call_param2
 // CHECK:STDOUT:     %return: ref <error> = return_slot %return.param
 // CHECK:STDOUT:   }
@@ -2710,8 +2710,8 @@ fn F() {
 // CHECK:STDOUT: !entry:
 // CHECK:STDOUT:   %F.ref: %F.type.f405c5.1 = name_ref F, @impl.4e9.%F.decl.loc30_33.1 [concrete = constants.%F.214a71.1]
 // CHECK:STDOUT:   %self.ref: %empty_tuple.type = name_ref self, %self.param
-// CHECK:STDOUT:   %.ref: <error> = name_ref <none>, %.param [concrete = <error>]
-// CHECK:STDOUT:   %return.ref: ref <error> = name_ref <return slot>, %return.param [concrete = <error>]
+// CHECK:STDOUT:   %.ref: <error> = name_ref <none>, %.param
+// CHECK:STDOUT:   %return.ref: ref <error> = name_ref <return slot>, %return.param
 // CHECK:STDOUT:   return <error>
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -2725,8 +2725,8 @@ fn F() {
 // CHECK:STDOUT: !entry:
 // CHECK:STDOUT:   %F.ref: %F.type.05d6a0.1 = name_ref F, @impl.8b3.%F.decl.loc39_33.1 [concrete = constants.%F.bfa759.1]
 // CHECK:STDOUT:   %self.ref: %C2 = name_ref self, %self.param
-// CHECK:STDOUT:   %.ref: <error> = name_ref <none>, %.param [concrete = <error>]
-// CHECK:STDOUT:   %return.ref: ref <error> = name_ref <return slot>, %return.param [concrete = <error>]
+// CHECK:STDOUT:   %.ref: <error> = name_ref <none>, %.param
+// CHECK:STDOUT:   %return.ref: ref <error> = name_ref <return slot>, %return.param
 // CHECK:STDOUT:   %F.bound: <bound method> = bound_method %self.ref, %F.ref
 // CHECK:STDOUT:   %F.call: init %C2 = call %F.bound(%self.ref, <error>)
 // CHECK:STDOUT:   return <error>
diff --git a/toolchain/check/testdata/interface/import_access.carbon b/toolchain/check/testdata/interface/import_access.carbon
index 2e411d15c971..94322dcb036b 100644
--- a/toolchain/check/testdata/interface/import_access.carbon
+++ b/toolchain/check/testdata/interface/import_access.carbon
@@ -264,7 +264,7 @@ private interface Redecl {}
 // CHECK:STDOUT:   } {
 // CHECK:STDOUT:     %i.param: <error> = value_param call_param0
 // CHECK:STDOUT:     %Def.ref: <error> = name_ref Def, <error> [concrete = <error>]
-// CHECK:STDOUT:     %i: <error> = bind_name i, %i.param [concrete = <error>]
+// CHECK:STDOUT:     %i: <error> = bind_name i, %i.param
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -302,7 +302,7 @@ private interface Redecl {}
 // CHECK:STDOUT:       %Test.ref: <namespace> = name_ref Test, imports.%Test [concrete = imports.%Test]
 // CHECK:STDOUT:       %Def.ref: <error> = name_ref Def, <error> [concrete = <error>]
 // CHECK:STDOUT:     }
-// CHECK:STDOUT:     %i: <error> = bind_name i, %i.param [concrete = <error>]
+// CHECK:STDOUT:     %i: <error> = bind_name i, %i.param
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -372,7 +372,7 @@ private interface Redecl {}
 // CHECK:STDOUT:   } {
 // CHECK:STDOUT:     %i.param: <error> = value_param call_param0
 // CHECK:STDOUT:     %ForwardWithDef.ref: <error> = name_ref ForwardWithDef, <error> [concrete = <error>]
-// CHECK:STDOUT:     %i: <error> = bind_name i, %i.param [concrete = <error>]
+// CHECK:STDOUT:     %i: <error> = bind_name i, %i.param
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -410,7 +410,7 @@ private interface Redecl {}
 // CHECK:STDOUT:       %Test.ref: <namespace> = name_ref Test, imports.%Test [concrete = imports.%Test]
 // CHECK:STDOUT:       %ForwardWithDef.ref: <error> = name_ref ForwardWithDef, <error> [concrete = <error>]
 // CHECK:STDOUT:     }
-// CHECK:STDOUT:     %i: <error> = bind_name i, %i.param [concrete = <error>]
+// CHECK:STDOUT:     %i: <error> = bind_name i, %i.param
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -444,7 +444,7 @@ private interface Redecl {}
 // CHECK:STDOUT:       %Forward.ref: <error> = name_ref Forward, <error> [concrete = <error>]
 // CHECK:STDOUT:       %ptr: type = ptr_type <error> [concrete = <error>]
 // CHECK:STDOUT:     }
-// CHECK:STDOUT:     %i: <error> = bind_name i, %i.param [concrete = <error>]
+// CHECK:STDOUT:     %i: <error> = bind_name i, %i.param
 // CHECK:STDOUT:   }
 // CHECK:STDOUT:   %Forward.decl: type = interface_decl @Forward [concrete = constants.%Forward.type] {} {}
 // CHECK:STDOUT: }
@@ -484,7 +484,7 @@ private interface Redecl {}
 // CHECK:STDOUT:       %Forward.ref: <error> = name_ref Forward, <error> [concrete = <error>]
 // CHECK:STDOUT:       %ptr: type = ptr_type <error> [concrete = <error>]
 // CHECK:STDOUT:     }
-// CHECK:STDOUT:     %i: <error> = bind_name i, %i.param [concrete = <error>]
+// CHECK:STDOUT:     %i: <error> = bind_name i, %i.param
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -522,7 +522,7 @@ private interface Redecl {}
 // CHECK:STDOUT:       %Forward.ref: <error> = name_ref Forward, <error> [concrete = <error>]
 // CHECK:STDOUT:       %ptr: type = ptr_type <error> [concrete = <error>]
 // CHECK:STDOUT:     }
-// CHECK:STDOUT:     %i: <error> = bind_name i, %i.param [concrete = <error>]
+// CHECK:STDOUT:     %i: <error> = bind_name i, %i.param
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/interop/cpp/class.carbon b/toolchain/check/testdata/interop/cpp/class.carbon
index 555b7d4dda56..3754b7694eda 100644
--- a/toolchain/check/testdata/interop/cpp/class.carbon
+++ b/toolchain/check/testdata/interop/cpp/class.carbon
@@ -410,7 +410,7 @@ fn MyF(bar: Cpp.Bar*);
 // CHECK:STDOUT:       %Bar.ref: <error> = name_ref Bar, <error> [concrete = <error>]
 // CHECK:STDOUT:       %ptr: type = ptr_type <error> [concrete = <error>]
 // CHECK:STDOUT:     }
-// CHECK:STDOUT:     %bar: <error> = bind_name bar, %bar.param [concrete = <error>]
+// CHECK:STDOUT:     %bar: <error> = bind_name bar, %bar.param
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -780,7 +780,7 @@ fn MyF(bar: Cpp.Bar*);
 // CHECK:STDOUT:       %Bar.ref: <error> = name_ref Bar, <error> [concrete = <error>]
 // CHECK:STDOUT:       %ptr: type = ptr_type <error> [concrete = <error>]
 // CHECK:STDOUT:     }
-// CHECK:STDOUT:     %bar: <error> = bind_name bar, %bar.param [concrete = <error>]
+// CHECK:STDOUT:     %bar: <error> = bind_name bar, %bar.param
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -865,7 +865,7 @@ fn MyF(bar: Cpp.Bar*);
 // CHECK:STDOUT:       %Bar.ref: <error> = name_ref Bar, <error> [concrete = <error>]
 // CHECK:STDOUT:       %ptr: type = ptr_type <error> [concrete = <error>]
 // CHECK:STDOUT:     }
-// CHECK:STDOUT:     %bar: <error> = bind_name bar, %bar.param [concrete = <error>]
+// CHECK:STDOUT:     %bar: <error> = bind_name bar, %bar.param
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/interop/cpp/function/class.carbon b/toolchain/check/testdata/interop/cpp/function/class.carbon
index d19bfa25c98d..fe40bf8d1945 100644
--- a/toolchain/check/testdata/interop/cpp/function/class.carbon
+++ b/toolchain/check/testdata/interop/cpp/function/class.carbon
@@ -828,7 +828,7 @@ fn F() {
 // CHECK:STDOUT: !entry:
 // CHECK:STDOUT:   %Cpp.ref.loc22: <namespace> = name_ref Cpp, imports.%Cpp [concrete = imports.%Cpp]
 // CHECK:STDOUT:   %foo.ref: <error> = name_ref foo, <error> [concrete = <error>]
-// CHECK:STDOUT:   %c.ref: <error> = name_ref c, %c [concrete = <error>]
+// CHECK:STDOUT:   %c.ref: <error> = name_ref c, %c
 // CHECK:STDOUT:   <elided>
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/interop/cpp/function/struct.carbon b/toolchain/check/testdata/interop/cpp/function/struct.carbon
index c5f19ffddebc..d6887bd83f6d 100644
--- a/toolchain/check/testdata/interop/cpp/function/struct.carbon
+++ b/toolchain/check/testdata/interop/cpp/function/struct.carbon
@@ -828,7 +828,7 @@ fn F() {
 // CHECK:STDOUT: !entry:
 // CHECK:STDOUT:   %Cpp.ref.loc22: <namespace> = name_ref Cpp, imports.%Cpp [concrete = imports.%Cpp]
 // CHECK:STDOUT:   %foo.ref: <error> = name_ref foo, <error> [concrete = <error>]
-// CHECK:STDOUT:   %s.ref: <error> = name_ref s, %s [concrete = <error>]
+// CHECK:STDOUT:   %s.ref: <error> = name_ref s, %s
 // CHECK:STDOUT:   <elided>
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/interop/cpp/function/union.carbon b/toolchain/check/testdata/interop/cpp/function/union.carbon
index 45a77a682790..76fd7468a13b 100644
--- a/toolchain/check/testdata/interop/cpp/function/union.carbon
+++ b/toolchain/check/testdata/interop/cpp/function/union.carbon
@@ -642,7 +642,7 @@ fn F() {
 // CHECK:STDOUT: !entry:
 // CHECK:STDOUT:   %Cpp.ref.loc22: <namespace> = name_ref Cpp, imports.%Cpp [concrete = imports.%Cpp]
 // CHECK:STDOUT:   %foo.ref: <error> = name_ref foo, <error> [concrete = <error>]
-// CHECK:STDOUT:   %u.ref: <error> = name_ref u, %u [concrete = <error>]
+// CHECK:STDOUT:   %u.ref: <error> = name_ref u, %u
 // CHECK:STDOUT:   <elided>
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/interop/cpp/struct.carbon b/toolchain/check/testdata/interop/cpp/struct.carbon
index 3cfaf7e79360..9fdfdc215f1a 100644
--- a/toolchain/check/testdata/interop/cpp/struct.carbon
+++ b/toolchain/check/testdata/interop/cpp/struct.carbon
@@ -400,7 +400,7 @@ fn MyF(bar: Cpp.Bar*);
 // CHECK:STDOUT:       %Bar.ref: <error> = name_ref Bar, <error> [concrete = <error>]
 // CHECK:STDOUT:       %ptr: type = ptr_type <error> [concrete = <error>]
 // CHECK:STDOUT:     }
-// CHECK:STDOUT:     %bar: <error> = bind_name bar, %bar.param [concrete = <error>]
+// CHECK:STDOUT:     %bar: <error> = bind_name bar, %bar.param
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -770,7 +770,7 @@ fn MyF(bar: Cpp.Bar*);
 // CHECK:STDOUT:       %Bar.ref: <error> = name_ref Bar, <error> [concrete = <error>]
 // CHECK:STDOUT:       %ptr: type = ptr_type <error> [concrete = <error>]
 // CHECK:STDOUT:     }
-// CHECK:STDOUT:     %bar: <error> = bind_name bar, %bar.param [concrete = <error>]
+// CHECK:STDOUT:     %bar: <error> = bind_name bar, %bar.param
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -855,7 +855,7 @@ fn MyF(bar: Cpp.Bar*);
 // CHECK:STDOUT:       %Bar.ref: <error> = name_ref Bar, <error> [concrete = <error>]
 // CHECK:STDOUT:       %ptr: type = ptr_type <error> [concrete = <error>]
 // CHECK:STDOUT:     }
-// CHECK:STDOUT:     %bar: <error> = bind_name bar, %bar.param [concrete = <error>]
+// CHECK:STDOUT:     %bar: <error> = bind_name bar, %bar.param
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/interop/cpp/union.carbon b/toolchain/check/testdata/interop/cpp/union.carbon
index c9b30f547a9f..08613ce542d8 100644
--- a/toolchain/check/testdata/interop/cpp/union.carbon
+++ b/toolchain/check/testdata/interop/cpp/union.carbon
@@ -294,7 +294,7 @@ fn MyF(bar: Cpp.Bar*);
 // CHECK:STDOUT:       %Bar.ref: <error> = name_ref Bar, <error> [concrete = <error>]
 // CHECK:STDOUT:       %ptr: type = ptr_type <error> [concrete = <error>]
 // CHECK:STDOUT:     }
-// CHECK:STDOUT:     %bar: <error> = bind_name bar, %bar.param [concrete = <error>]
+// CHECK:STDOUT:     %bar: <error> = bind_name bar, %bar.param
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -552,7 +552,7 @@ fn MyF(bar: Cpp.Bar*);
 // CHECK:STDOUT:       %Bar.ref: <error> = name_ref Bar, <error> [concrete = <error>]
 // CHECK:STDOUT:       %ptr: type = ptr_type <error> [concrete = <error>]
 // CHECK:STDOUT:     }
-// CHECK:STDOUT:     %bar: <error> = bind_name bar, %bar.param [concrete = <error>]
+// CHECK:STDOUT:     %bar: <error> = bind_name bar, %bar.param
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/namespace/fail_params.carbon b/toolchain/check/testdata/namespace/fail_params.carbon
index 686ecc0a29ce..41a0e7554feb 100644
--- a/toolchain/check/testdata/namespace/fail_params.carbon
+++ b/toolchain/check/testdata/namespace/fail_params.carbon
@@ -81,7 +81,7 @@ fn D(T:! type).F() {}
 // CHECK:STDOUT:   %F.decl.loc22: %F.type.bd7 = fn_decl @F.1 [concrete = constants.%F.199] {} {}
 // CHECK:STDOUT:   %n.param: <error> = value_param call_param0
 // CHECK:STDOUT:   %int_32: Core.IntLiteral = int_value 32 [concrete = constants.%int_32]
-// CHECK:STDOUT:   %n: <error> = bind_name n, %n.param [concrete = <error>]
+// CHECK:STDOUT:   %n: <error> = bind_name n, %n.param
 // CHECK:STDOUT:   %B: <namespace> = namespace [concrete] {}
 // CHECK:STDOUT:   %T: type = bind_symbolic_name T, 0 [symbolic = constants.%T]
 // CHECK:STDOUT:   %x.param: %T = value_param call_param0
diff --git a/toolchain/check/testdata/pointer/fail_deref_not_pointer.carbon b/toolchain/check/testdata/pointer/fail_deref_not_pointer.carbon
index c3ff74e86000..15d091e53c60 100644
--- a/toolchain/check/testdata/pointer/fail_deref_not_pointer.carbon
+++ b/toolchain/check/testdata/pointer/fail_deref_not_pointer.carbon
@@ -92,9 +92,9 @@ fn Deref(n: i32) {
 // CHECK:STDOUT: fn @Deref(%n.param: %i32) {
 // CHECK:STDOUT: !entry:
 // CHECK:STDOUT:   %n.ref.loc20: %i32 = name_ref n, %n
-// CHECK:STDOUT:   %.loc20: ref <error> = deref %n.ref.loc20 [concrete = <error>]
+// CHECK:STDOUT:   %.loc20: ref <error> = deref %n.ref.loc20
 // CHECK:STDOUT:   %n.ref.loc25: %i32 = name_ref n, %n
-// CHECK:STDOUT:   %.loc25: ref <error> = deref %n.ref.loc25 [concrete = <error>]
+// CHECK:STDOUT:   %.loc25: ref <error> = deref %n.ref.loc25
 // CHECK:STDOUT:   %foo.ref.loc25: <error> = name_ref foo, <error> [concrete = <error>]
 // CHECK:STDOUT:   %.loc30_5.1: %empty_tuple.type = tuple_literal ()
 // CHECK:STDOUT:   %empty_tuple.loc30: %empty_tuple.type = tuple_value () [concrete = constants.%empty_tuple]