Index: libcxxabi/src/demangle/ItaniumDemangle.h
===================================================================
--- libcxxabi/src/demangle/ItaniumDemangle.h
+++ libcxxabi/src/demangle/ItaniumDemangle.h
@@ -2587,39 +2587,44 @@
 Node *AbstractManglingParser<Derived, Alloc>::parseName(NameState *State) {
   consumeIf('L'); // extension
 
-  if (look() == 'N')
-    return getDerived().parseNestedName(State);
-  if (look() == 'Z')
-    return getDerived().parseLocalName(State);
-
-  //        ::= <unscoped-template-name> <template-args>
-  if (look() == 'S' && look(1) != 't') {
-    Node *S = getDerived().parseSubstitution();
-    if (S == nullptr)
-      return nullptr;
-    if (look() != 'I')
-      return nullptr;
-    Node *TA = getDerived().parseTemplateArgs(State != nullptr);
-    if (TA == nullptr)
+  Node *Result = nullptr;
+  if (look() == 'N') {
+    Result = getDerived().parseNestedName(State);
+  } else if (look() == 'Z') {
+    Result = getDerived().parseLocalName(State);
+  } else {
+    bool IsSubst = look() == 'S' && look(1) != 't';
+    if (IsSubst) {
+      // A substitution must lead to:
+      //        ::= <unscoped-template-name> <template-args>
+      Result = getDerived().parseSubstitution();
+    } else {
+      // An unscoped name can be one of:
+      //        ::= <unscoped-name>
+      //        ::= <unscoped-template-name> <template-args>
+      Result = getDerived().parseUnscopedName(State);
+    }
+    if (Result == nullptr)
       return nullptr;
-    if (State) State->EndsWithTemplateArgs = true;
-    return make<NameWithTemplateArgs>(S, TA);
-  }
 
-  Node *N = getDerived().parseUnscopedName(State);
-  if (N == nullptr)
-    return nullptr;
-  //        ::= <unscoped-template-name> <template-args>
-  if (look() == 'I') {
-    Subs.push_back(N);
-    Node *TA = getDerived().parseTemplateArgs(State != nullptr);
-    if (TA == nullptr)
+    if (look() == 'I') {
+      //        ::= <unscoped-template-name> <template-args>
+      if (!IsSubst)
+        // An unscoped-template-name is substitutable.
+        Subs.push_back(Result);
+      Node *TA = getDerived().parseTemplateArgs(State != nullptr);
+      if (TA == nullptr)
+        return nullptr;
+      if (State)
+        State->EndsWithTemplateArgs = true;
+      Result = make<NameWithTemplateArgs>(Result, TA);
+    } else if (IsSubst) {
+      // The substitution case must be followed by template-args
       return nullptr;
-    if (State) State->EndsWithTemplateArgs = true;
-    return make<NameWithTemplateArgs>(N, TA);
+    }
   }
-  //        ::= <unscoped-name>
-  return N;
+
+  return Result;
 }
 
 // <local-name> := Z <function encoding> E <entity name> [<discriminator>]
@@ -2664,13 +2669,17 @@
 template <typename Derived, typename Alloc>
 Node *
 AbstractManglingParser<Derived, Alloc>::parseUnscopedName(NameState *State) {
-  if (consumeIf("StL") || consumeIf("St")) {
-    Node *R = getDerived().parseUnqualifiedName(State);
-    if (R == nullptr)
-      return nullptr;
-    return make<StdQualifiedName>(R);
-  }
-  return getDerived().parseUnqualifiedName(State);
+  bool IsStd = consumeIf("St");
+  if (IsStd)
+    consumeIf('L');
+
+  Node *Result = getDerived().parseUnqualifiedName(State);
+  if (Result == nullptr)
+    return nullptr;
+  if (IsStd)
+    Result = make<StdQualifiedName>(Result);
+
+  return Result;
 }
 
 // <unqualified-name> ::= <operator-name> [abi-tags]
@@ -4065,9 +4074,9 @@
   }
   //             ::= <substitution>  # See Compression below
   case 'S': {
-    if (look(1) && look(1) != 't') {
-      Node *Sub = getDerived().parseSubstitution();
-      if (Sub == nullptr)
+    if (look(1) != 't') {
+      Result = getDerived().parseSubstitution();
+      if (Result == nullptr)
         return nullptr;
 
       // Sub could be either of:
@@ -4084,13 +4093,13 @@
         Node *TA = getDerived().parseTemplateArgs();
         if (TA == nullptr)
           return nullptr;
-        Result = make<NameWithTemplateArgs>(Sub, TA);
-        break;
+        Result = make<NameWithTemplateArgs>(Result, TA);
+      } else {
+        // If all we parsed was a substitution, don't re-insert into the
+        // substitution table.
+        return Result;
       }
-
-      // If all we parsed was a substitution, don't re-insert into the
-      // substitution table.
-      return Sub;
+      break;
     }
     DEMANGLE_FALLTHROUGH;
   }
Index: libcxxabi/test/test_demangle.pass.cpp
===================================================================
--- libcxxabi/test/test_demangle.pass.cpp
+++ libcxxabi/test/test_demangle.pass.cpp
@@ -29855,6 +29855,8 @@
     // This should be invalid, but it is currently not recognized as such
     // See https://llvm.org/PR51407
     {"_Zcv1BIRT_EIS1_E", "operator B<><>"},
+
+    {"_Z3TPLIiET_S0_", "int TPL<int>(int)"},
 };
 
 const unsigned N = sizeof(cases) / sizeof(cases[0]);
Index: llvm/include/llvm/Demangle/ItaniumDemangle.h
===================================================================
--- llvm/include/llvm/Demangle/ItaniumDemangle.h
+++ llvm/include/llvm/Demangle/ItaniumDemangle.h
@@ -2587,39 +2587,44 @@
 Node *AbstractManglingParser<Derived, Alloc>::parseName(NameState *State) {
   consumeIf('L'); // extension
 
-  if (look() == 'N')
-    return getDerived().parseNestedName(State);
-  if (look() == 'Z')
-    return getDerived().parseLocalName(State);
-
-  //        ::= <unscoped-template-name> <template-args>
-  if (look() == 'S' && look(1) != 't') {
-    Node *S = getDerived().parseSubstitution();
-    if (S == nullptr)
-      return nullptr;
-    if (look() != 'I')
-      return nullptr;
-    Node *TA = getDerived().parseTemplateArgs(State != nullptr);
-    if (TA == nullptr)
+  Node *Result = nullptr;
+  if (look() == 'N') {
+    Result = getDerived().parseNestedName(State);
+  } else if (look() == 'Z') {
+    Result = getDerived().parseLocalName(State);
+  } else {
+    bool IsSubst = look() == 'S' && look(1) != 't';
+    if (IsSubst) {
+      // A substitution must lead to:
+      //        ::= <unscoped-template-name> <template-args>
+      Result = getDerived().parseSubstitution();
+    } else {
+      // An unscoped name can be one of:
+      //        ::= <unscoped-name>
+      //        ::= <unscoped-template-name> <template-args>
+      Result = getDerived().parseUnscopedName(State);
+    }
+    if (Result == nullptr)
       return nullptr;
-    if (State) State->EndsWithTemplateArgs = true;
-    return make<NameWithTemplateArgs>(S, TA);
-  }
 
-  Node *N = getDerived().parseUnscopedName(State);
-  if (N == nullptr)
-    return nullptr;
-  //        ::= <unscoped-template-name> <template-args>
-  if (look() == 'I') {
-    Subs.push_back(N);
-    Node *TA = getDerived().parseTemplateArgs(State != nullptr);
-    if (TA == nullptr)
+    if (look() == 'I') {
+      //        ::= <unscoped-template-name> <template-args>
+      if (!IsSubst)
+        // An unscoped-template-name is substitutable.
+        Subs.push_back(Result);
+      Node *TA = getDerived().parseTemplateArgs(State != nullptr);
+      if (TA == nullptr)
+        return nullptr;
+      if (State)
+        State->EndsWithTemplateArgs = true;
+      Result = make<NameWithTemplateArgs>(Result, TA);
+    } else if (IsSubst) {
+      // The substitution case must be followed by template-args
       return nullptr;
-    if (State) State->EndsWithTemplateArgs = true;
-    return make<NameWithTemplateArgs>(N, TA);
+    }
   }
-  //        ::= <unscoped-name>
-  return N;
+
+  return Result;
 }
 
 // <local-name> := Z <function encoding> E <entity name> [<discriminator>]
@@ -2664,13 +2669,17 @@
 template <typename Derived, typename Alloc>
 Node *
 AbstractManglingParser<Derived, Alloc>::parseUnscopedName(NameState *State) {
-  if (consumeIf("StL") || consumeIf("St")) {
-    Node *R = getDerived().parseUnqualifiedName(State);
-    if (R == nullptr)
-      return nullptr;
-    return make<StdQualifiedName>(R);
-  }
-  return getDerived().parseUnqualifiedName(State);
+  bool IsStd = consumeIf("St");
+  if (IsStd)
+    consumeIf('L');
+
+  Node *Result = getDerived().parseUnqualifiedName(State);
+  if (Result == nullptr)
+    return nullptr;
+  if (IsStd)
+    Result = make<StdQualifiedName>(Result);
+
+  return Result;
 }
 
 // <unqualified-name> ::= <operator-name> [abi-tags]
@@ -4065,9 +4074,9 @@
   }
   //             ::= <substitution>  # See Compression below
   case 'S': {
-    if (look(1) && look(1) != 't') {
-      Node *Sub = getDerived().parseSubstitution();
-      if (Sub == nullptr)
+    if (look(1) != 't') {
+      Result = getDerived().parseSubstitution();
+      if (Result == nullptr)
         return nullptr;
 
       // Sub could be either of:
@@ -4084,13 +4093,13 @@
         Node *TA = getDerived().parseTemplateArgs();
         if (TA == nullptr)
           return nullptr;
-        Result = make<NameWithTemplateArgs>(Sub, TA);
-        break;
+        Result = make<NameWithTemplateArgs>(Result, TA);
+      } else {
+        // If all we parsed was a substitution, don't re-insert into the
+        // substitution table.
+        return Result;
       }
-
-      // If all we parsed was a substitution, don't re-insert into the
-      // substitution table.
-      return Sub;
+      break;
     }
     DEMANGLE_FALLTHROUGH;
   }