diff --git a/src/demangle/ItaniumDemangle.h b/src/demangle/ItaniumDemangle.h
index c8a77ad..d0eaf6d 100644
--- a/src/demangle/ItaniumDemangle.h
+++ b/src/demangle/ItaniumDemangle.h
@@ -2572,8 +2572,6 @@
 //                          ::= <substitution>
 template <typename Derived, typename Alloc>
 Node *AbstractManglingParser<Derived, Alloc>::parseName(NameState *State) {
-  consumeIf('L'); // extension
-
   if (look() == 'N')
     return getDerived().parseNestedName(State);
   if (look() == 'Z')
@@ -2649,15 +2647,14 @@
   return make<LocalName>(Encoding, Entity);
 }
 
-// <unscoped-name> ::= <unqualified-name>
-//                 ::= St <unqualified-name>   # ::std::
-// extension       ::= StL<unqualified-name>
+// <unscoped-name> ::= [L]* <unqualified-name>
+//                 ::= St [L]* <unqualified-name>   # ::std::
+// [*] extension
 template <typename Derived, typename Alloc>
 Node *
 AbstractManglingParser<Derived, Alloc>::parseUnscopedName(NameState *State) {
   bool IsStd = consumeIf("St");
-  if (IsStd)
-    consumeIf('L');
+  consumeIf('L');
 
   Node *Result = getDerived().parseUnqualifiedName(State);
   if (Result == nullptr)
@@ -3148,14 +3145,14 @@
 // <nested-name> ::= N [<CV-Qualifiers>] [<ref-qualifier>] <prefix> <unqualified-name> E
 //               ::= N [<CV-Qualifiers>] [<ref-qualifier>] <template-prefix> <template-args> E
 //
-// <prefix> ::= <prefix> <unqualified-name>
+// <prefix> ::= <prefix> [L]* <unqualified-name>
 //          ::= <template-prefix> <template-args>
 //          ::= <template-param>
 //          ::= <decltype>
 //          ::= # empty
 //          ::= <substitution>
 //          ::= <prefix> <data-member-prefix>
-//  extension ::= L
+// [*] extension
 //
 // <data-member-prefix> := <member source-name> [<template-args>] M
 //
@@ -3175,88 +3172,85 @@
     if (State) State->ReferenceQualifier = FrefQualRValue;
   } else if (consumeIf('R')) {
     if (State) State->ReferenceQualifier = FrefQualLValue;
-  } else
+  } else {
     if (State) State->ReferenceQualifier = FrefQualNone;
-
-  Node *SoFar = nullptr;
-  auto PushComponent = [&](Node *Comp) {
-    if (!Comp) return false;
-    if (SoFar) SoFar = make<NestedName>(SoFar, Comp);
-    else       SoFar = Comp;
-    if (State) State->EndsWithTemplateArgs = false;
-    return SoFar != nullptr;
-  };
-
-  if (consumeIf("St")) {
-    SoFar = make<NameType>("std");
-    if (!SoFar)
-      return nullptr;
   }
 
+  Node *SoFar = nullptr;
   while (!consumeIf('E')) {
     consumeIf('L'); // extension
 
-    // <data-member-prefix> := <member source-name> [<template-args>] M
     if (consumeIf('M')) {
+      // <data-member-prefix> := <member source-name> [<template-args>] M
       if (SoFar == nullptr)
         return nullptr;
       continue;
     }
 
-    //          ::= <template-param>
+    if (State)
+      // Only set end-with-template on the case that does that.
+      State->EndsWithTemplateArgs = false;
+
     if (look() == 'T') {
-      if (!PushComponent(getDerived().parseTemplateParam()))
-        return nullptr;
-      Subs.push_back(SoFar);
-      continue;
-    }
-
-    //          ::= <template-prefix> <template-args>
-    if (look() == 'I') {
+      //          ::= <template-param>
+      if (SoFar != nullptr)
+        return nullptr; // Cannot have a prefix.
+      SoFar = getDerived().parseTemplateParam();
+    } else if (look() == 'I') {
+      //          ::= <template-prefix> <template-args>
+      if (SoFar == nullptr)
+        return nullptr; // Must have a prefix.
       Node *TA = getDerived().parseTemplateArgs(State != nullptr);
-      if (TA == nullptr || SoFar == nullptr)
+      if (TA == nullptr)
         return nullptr;
+      if (SoFar->getKind() == Node::KNameWithTemplateArgs)
+        // Semantically <template-args> <template-args> cannot be generated by a
+        // C++ entity.  There will always be [something like] a name between
+        // them.
+        return nullptr;
+      if (State)
+        State->EndsWithTemplateArgs = true;
       SoFar = make<NameWithTemplateArgs>(SoFar, TA);
-      if (!SoFar)
-        return nullptr;
-      if (State) State->EndsWithTemplateArgs = true;
-      Subs.push_back(SoFar);
-      continue;
-    }
-
-    //          ::= <decltype>
-    if (look() == 'D' && (look(1) == 't' || look(1) == 'T')) {
-      if (!PushComponent(getDerived().parseDecltype()))
-        return nullptr;
-      Subs.push_back(SoFar);
-      continue;
-    }
-
-    //          ::= <substitution>
-    if (look() == 'S' && look(1) != 't') {
-      Node *S = getDerived().parseSubstitution();
-      if (!PushComponent(S))
-        return nullptr;
-      if (SoFar != S)
-        Subs.push_back(S);
-      continue;
-    }
-
-    // Parse an <unqualified-name> thats actually a <ctor-dtor-name>.
-    if (look() == 'C' || (look() == 'D' && look(1) != 'C')) {
+    } else if (look() == 'D' && (look(1) == 't' || look(1) == 'T')) {
+      //          ::= <decltype>
+      if (SoFar != nullptr)
+        return nullptr; // Cannot have a prefix.
+      SoFar = getDerived().parseDecltype();
+    } else if (look() == 'S') {
+      //          ::= <substitution>
+      if (SoFar != nullptr)
+        return nullptr; // Cannot have a prefix.
+      if (look(1) == 't') {
+        // parseSubstition does not handle 'St'.
+        First += 2;
+        SoFar = make<NameType>("std");
+      } else {
+        SoFar = getDerived().parseSubstitution();
+      }
       if (SoFar == nullptr)
         return nullptr;
-      if (!PushComponent(getDerived().parseCtorDtorName(SoFar, State)))
+      continue; // Do not push a new substitution.
+    } else {
+      Node *N = nullptr;
+      if (look() == 'C' || (look() == 'D' && look(1) != 'C')) {
+        // An <unqualified-name> that's actually a <ctor-dtor-name>.
+        if (SoFar == nullptr)
+          return nullptr;
+        N = getDerived().parseCtorDtorName(SoFar, State);
+        if (N != nullptr)
+          N = getDerived().parseAbiTags(N);
+      } else {
+        //          ::= <prefix> <unqualified-name>
+        N = getDerived().parseUnqualifiedName(State);
+      }
+      if (N == nullptr)
         return nullptr;
-      SoFar = getDerived().parseAbiTags(SoFar);
-      if (SoFar == nullptr)
-        return nullptr;
-      Subs.push_back(SoFar);
-      continue;
+      if (SoFar)
+        SoFar = make<NestedName>(SoFar, N);
+      else
+        SoFar = N;
     }
-
-    //          ::= <prefix> <unqualified-name>
-    if (!PushComponent(getDerived().parseUnqualifiedName(State)))
+    if (SoFar == nullptr)
       return nullptr;
     Subs.push_back(SoFar);
   }
@@ -5431,6 +5425,7 @@
 // <substitution> ::= Si # ::std::basic_istream<char,  std::char_traits<char> >
 // <substitution> ::= So # ::std::basic_ostream<char,  std::char_traits<char> >
 // <substitution> ::= Sd # ::std::basic_iostream<char, std::char_traits<char> >
+// The St case is handled specially in parseNestedName.
 template <typename Derived, typename Alloc>
 Node *AbstractManglingParser<Derived, Alloc>::parseSubstitution() {
   if (!consumeIf('S'))
diff --git a/test/test_demangle.pass.cpp b/test/test_demangle.pass.cpp
index 191b4b6..263494a 100644
--- a/test/test_demangle.pass.cpp
+++ b/test/test_demangle.pass.cpp
@@ -29936,6 +29936,11 @@
     "FSiIJEENT_IoE ",
     "ZTVSiIZTVSiIZTVSiIZTVSiINIJEET_T_T_T_T_ ",
     "Ana_T_E_T_IJEffffffffffffffersfffffrsrsffffffbgE",
+
+    "_ZN3TPLS_E",
+    "_ZN3CLSIiEIiEE",
+    "_ZN3CLSDtLi0EEE",
+    "_ZN3CLSIiEEvNS_T_Ev",
 };
 
 const unsigned NI = sizeof(invalid_cases) / sizeof(invalid_cases[0]);