diff --git a/toolchain/check/testdata/const/basics.carbon b/toolchain/check/testdata/const/basics.carbon
index ae45324a465c..106f69b659e6 100644
--- a/toolchain/check/testdata/const/basics.carbon
+++ b/toolchain/check/testdata/const/basics.carbon
@@ -127,6 +127,45 @@ fn PassConstReferenceToReference(p: const X*) {
   p->(X.TakeSelf)();
 }
 
+// --- fail_print_const_facet_type.carbon
+library "[[@TEST_NAME]]";
+
+interface I { let T: type; }
+interface J {}
+
+// A redeclaration with a mismatched return type prints the original return
+// type. The operand of `const` is parenthesized if it's a facet type formed
+// with `&` or `where`.
+fn F() -> const (I & J);
+// CHECK:STDERR: fail_print_const_facet_type.carbon:[[@LINE+7]]:1: error: function redeclaration differs because return type is `{}` [FunctionRedeclReturnTypeDiffers]
+// CHECK:STDERR: fn F() -> {};
+// CHECK:STDERR: ^~~~~~~~~~~~~
+// CHECK:STDERR: fail_print_const_facet_type.carbon:[[@LINE-4]]:1: note: previously declared with return type `const (I & J)` [FunctionRedeclReturnTypePrevious]
+// CHECK:STDERR: fn F() -> const (I & J);
+// CHECK:STDERR: ^~~~~~~~~~~~~~~~~~~~~~~~
+// CHECK:STDERR:
+fn F() -> {};
+
+fn G() -> const (I where .T = ());
+// CHECK:STDERR: fail_print_const_facet_type.carbon:[[@LINE+7]]:1: error: function redeclaration differs because return type is `{}` [FunctionRedeclReturnTypeDiffers]
+// CHECK:STDERR: fn G() -> {};
+// CHECK:STDERR: ^~~~~~~~~~~~~
+// CHECK:STDERR: fail_print_const_facet_type.carbon:[[@LINE-4]]:1: note: previously declared with return type `const (I where .(I.T) = ())` [FunctionRedeclReturnTypePrevious]
+// CHECK:STDERR: fn G() -> const (I where .T = ());
+// CHECK:STDERR: ^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+// CHECK:STDERR:
+fn G() -> {};
+
+// No parentheses are needed for a single interface.
+fn H() -> const I;
+// CHECK:STDERR: fail_print_const_facet_type.carbon:[[@LINE+7]]:1: error: function redeclaration differs because return type is `{}` [FunctionRedeclReturnTypeDiffers]
+// CHECK:STDERR: fn H() -> {};
+// CHECK:STDERR: ^~~~~~~~~~~~~
+// CHECK:STDERR: fail_print_const_facet_type.carbon:[[@LINE-4]]:1: note: previously declared with return type `const I` [FunctionRedeclReturnTypePrevious]
+// CHECK:STDERR: fn H() -> const I;
+// CHECK:STDERR: ^~~~~~~~~~~~~~~~~~
+// CHECK:STDERR:
+fn H() -> {};
 
 // CHECK:STDOUT: --- basic.carbon
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/eval/symbolic.carbon b/toolchain/check/testdata/eval/symbolic.carbon
index 284b77718348..26f1baebfbf5 100644
--- a/toolchain/check/testdata/eval/symbolic.carbon
+++ b/toolchain/check/testdata/eval/symbolic.carbon
@@ -145,6 +145,24 @@ fn UseM(generic c: C, x: c.M(true));
 // CHECK:STDERR:
 fn UseM(generic c: C, x: bool);
 
+// Parentheses are added around the `self` argument if needed.
+interface J {
+  eval fn N(self: Self) -> type;
+}
+impl type as J {
+  eval fn N(self: Self) -> type { return self; }
+}
+
+fn UseN(generic T: type, x: (const T).(J.N)());
+// CHECK:STDERR: fail_print_call_in_diagnostic.carbon:[[@LINE+7]]:26: error: type `<pattern for bool>` of parameter 2 in redeclaration differs from previous parameter type `<pattern for (const T).N()>` [RedeclParamDiffersType]
+// CHECK:STDERR: fn UseN(generic T: type, x: bool);
+// CHECK:STDERR:                          ^~~~~~~
+// CHECK:STDERR: fail_print_call_in_diagnostic.carbon:[[@LINE-4]]:26: note: previous declaration's corresponding parameter here [RedeclParamPrevious]
+// CHECK:STDERR: fn UseN(generic T: type, x: (const T).(J.N)());
+// CHECK:STDERR:                          ^~~~~~~~~~~~~~~~~~~~
+// CHECK:STDERR:
+fn UseN(generic T: type, x: bool);
+
 // CHECK:STDOUT: --- dependent_symbolic_instruction.carbon
 // CHECK:STDOUT:
 // CHECK:STDOUT: constants {
diff --git a/toolchain/sem_ir/stringify.cpp b/toolchain/sem_ir/stringify.cpp
index 2927f66187b0..f0035beed8cb 100644
--- a/toolchain/sem_ir/stringify.cpp
+++ b/toolchain/sem_ir/stringify.cpp
@@ -25,18 +25,82 @@
 
 namespace Carbon::SemIR {
 
-// Map an instruction kind representing an expression into an integer describing
-// the precedence of that expression's syntax. Higher numbers correspond to
-// higher precedence.
-static auto GetPrecedence(InstKind kind) -> int {
-  if (kind == ConstType::Kind) {
-    return -1;
+// Precedence levels for the syntax produced when stringifying an instruction.
+// Higher numbers correspond to higher precedence. An operand needs to be
+// parenthesized if its precedence is lower than that required by the enclosing
+// syntax.
+//
+// Carbon's precedence is a partial order, not a total order, but the only
+// enclosing syntax that we currently check for is prefix and postfix operators,
+// which have higher precedence than all infix operators, so a total order
+// suffices for now.
+enum class Precedence : int8_t {
+  // `A where ...`
+  Where = -5,
+  // `A & B`
+  BitwiseAnd = -4,
+  // `A as B`
+  As = -3,
+  // `T*`
+  PostfixStar = -2,
+  // `const T`, `partial T`
+  PrefixType = -1,
+  // Names, literals, calls, member access, and anything parenthesized or
+  // otherwise bracketed.
+  Primary = 0,
+};
+
+// Returns the precedence of the syntax that stringifying `inst_id` produces.
+static auto GetPrecedence(const File& sem_ir, InstId inst_id) -> Precedence {
+  while (inst_id.has_value()) {
+    auto inst = sem_ir.insts().Get(inst_id);
+    switch (inst.kind()) {
+      case Call::Kind:
+      case TypeOfInst::Kind: {
+        // These print their constant value instead, if it's different.
+        auto const_inst_id =
+            sem_ir.constant_values().GetConstantInstId(inst_id);
+        if (!const_inst_id.has_value() || const_inst_id == inst_id) {
+          return Precedence::Primary;
+        }
+        inst_id = const_inst_id;
+        break;
+      }
+      case FacetAccessType::Kind: {
+        inst_id = inst.As<FacetAccessType>().facet_value_inst_id;
+        break;
+      }
+      case FacetType::Kind: {
+        const auto& info = sem_ir.declared_facet_types().Get(
+            inst.As<FacetType>().declared_facet_type_id);
+        if (info.other_requirements || !info.rewrite_constraints.empty() ||
+            !info.self_impls_constraints.empty() ||
+            !info.self_impls_named_constraints.empty() ||
+            !info.type_impls_interfaces.empty() ||
+            !info.type_impls_named_constraints.empty()) {
+          return Precedence::Where;
+        }
+        if (info.extend_constraints.size() +
+                info.extend_named_constraints.size() >
+            1) {
+          return Precedence::BitwiseAnd;
+        }
+        return Precedence::Primary;
+      }
+      case FacetValue::Kind:
+      case LookupImplWitness::Kind:
+        return Precedence::As;
+      case PointerType::Kind:
+        return Precedence::PostfixStar;
+      case ConstType::Kind:
+      case PartialType::Kind:
+        return Precedence::PrefixType;
+      default:
+        // TODO: Handle other kinds of expressions with precedence.
+        return Precedence::Primary;
+    }
   }
-  if (kind == PointerType::Kind) {
-    return -2;
-  }
-  // TODO: Handle other kinds of expressions with precedence.
-  return 0;
+  return Precedence::Primary;
 }
 
 namespace {
@@ -532,8 +596,7 @@ class Stringifier {
     }
 
     // Add parentheses if required.
-    if (GetPrecedence(sem_ir_->insts().Get(inner_id).kind()) <
-        GetPrecedence(ConstType::Kind)) {
+    if (GetPrecedence(*sem_ir_, inner_id) < Precedence::PrefixType) {
       *out_ << "(";
       // Note the `inner_id` ends up here.
       step_stack_->PushString(")");