diff --git a/Units/parser-cxx.r/template-member-function-pointer-scope.d/args.ctags b/Units/parser-cxx.r/template-member-function-pointer-scope.d/args.ctags
new file mode 100644
index 0000000000..7d2ba98655
--- /dev/null
+++ b/Units/parser-cxx.r/template-member-function-pointer-scope.d/args.ctags
@@ -0,0 +1,3 @@
+--sort=no
+--fields=+{signature}
+--kinds-C++=+fstz
diff --git a/Units/parser-cxx.r/template-member-function-pointer-scope.d/expected.tags b/Units/parser-cxx.r/template-member-function-pointer-scope.d/expected.tags
new file mode 100644
index 0000000000..1ef6bca107
--- /dev/null
+++ b/Units/parser-cxx.r/template-member-function-pointer-scope.d/expected.tags
@@ -0,0 +1,19 @@
+TestUtil	input.cpp	/^struct TestUtil {$/;"	s	file:
+isNull	input.cpp	/^    static bool isNull(const T&) { return false; }$/;"	f	struct:TestUtil	typeref:typename:bool	file:	signature:(const T &)
+__anon39cbdfcb010d	input.cpp	/^    static bool isNull(const T&) { return false; }$/;"	z	function:TestUtil::isNull	typeref:typename:const T &	file:
+TestUtil	input.cpp	/^struct TestUtil<T*> {$/;"	s	file:
+isNull	input.cpp	/^    static bool isNull(T* f) { return 0 == f; }$/;"	f	struct:TestUtil	typeref:typename:bool	file:	signature:(T * f)
+f	input.cpp	/^    static bool isNull(T* f) { return 0 == f; }$/;"	z	function:TestUtil::isNull	typeref:typename:T *	file:
+memtype	input.cpp	/^struct memtype {};$/;"	s	file:
+klass	input.cpp	/^struct klass {};$/;"	s	file:
+isNull	input.cpp	/^TestUtil<const memtype klass::*&>::isNull(const memtype klass::* &f)$/;"	f	class:TestUtil	typeref:typename:bool	signature:(const memtype klass::* & f)
+f	input.cpp	/^TestUtil<const memtype klass::*&>::isNull(const memtype klass::* &f)$/;"	z	function:TestUtil::isNull	typeref:typename:const memtype klass::* &	file:
+Handler	input.cpp	/^struct Handler {$/;"	s	file:
+process	input.cpp	/^    void process(T value) { }$/;"	f	struct:Handler	typeref:typename:void	file:	signature:(T value)
+value	input.cpp	/^    void process(T value) { }$/;"	z	function:Handler::process	typeref:typename:T	file:
+Handler	input.cpp	/^struct Handler<R (C::*)()> {$/;"	s	file:
+process	input.cpp	/^    void process(R (C::*method)()) { }$/;"	f	struct:Handler	typeref:typename:void	file:	signature:(R (C::* method)())
+method	input.cpp	/^    void process(R (C::*method)()) { }$/;"	z	function:Handler::process	typeref:typename:R (C::*)()	file:
+Handler	input.cpp	/^struct Handler<R (C::*)(A)> {$/;"	s	file:
+process	input.cpp	/^    void process(R (C::*method)(A)) { }$/;"	f	struct:Handler	typeref:typename:void	file:	signature:(R (C::* method)(A))
+method	input.cpp	/^    void process(R (C::*method)(A)) { }$/;"	z	function:Handler::process	typeref:typename:R (C::*)(A)	file:
diff --git a/Units/parser-cxx.r/template-member-function-pointer-scope.d/input.cpp b/Units/parser-cxx.r/template-member-function-pointer-scope.d/input.cpp
new file mode 100644
index 0000000000..9e0e7b08d5
--- /dev/null
+++ b/Units/parser-cxx.r/template-member-function-pointer-scope.d/input.cpp
@@ -0,0 +1,40 @@
+// Derived from #4348 submitted by @gaborbernat.
+
+// C++ template specialization that previously triggered scope management crash
+// Test case for issue 4344: assertion failure in cxxScopePushTop
+template <class T>
+struct TestUtil {
+    static bool isNull(const T&) { return false; }
+};
+
+template <class T>
+struct TestUtil<T*> {
+    static bool isNull(T* f) { return 0 == f; }
+};
+
+struct memtype {};
+struct klass {};
+
+template <>
+inline
+bool
+TestUtil<const memtype klass::*&>::isNull(const memtype klass::* &f)
+{
+    return 0 == f;
+}
+
+// Additional test cases for complex template specializations
+template <typename T>
+struct Handler {
+    void process(T value) { }
+};
+
+template <typename R, typename C>
+struct Handler<R (C::*)()> {
+    void process(R (C::*method)()) { }
+};
+
+template <typename R, typename C, typename A>
+struct Handler<R (C::*)(A)> {
+    void process(R (C::*method)(A)) { }
+};
diff --git a/Units/parser-cxx.r/template-member-function-pointer-scope.d/validator b/Units/parser-cxx.r/template-member-function-pointer-scope.d/validator
new file mode 100644
index 0000000000..30c863ebde
--- /dev/null
+++ b/Units/parser-cxx.r/template-member-function-pointer-scope.d/validator
@@ -0,0 +1 @@
+cxx11
diff --git a/Units/parser-cxx.r/template-specializations-including-op.d/args.ctags b/Units/parser-cxx.r/template-specializations-including-op.d/args.ctags
new file mode 100644
index 0000000000..5ee5f79f70
--- /dev/null
+++ b/Units/parser-cxx.r/template-specializations-including-op.d/args.ctags
@@ -0,0 +1 @@
+--sort=no
diff --git a/Units/parser-cxx.r/template-specializations-including-op.d/expected.tags b/Units/parser-cxx.r/template-specializations-including-op.d/expected.tags
new file mode 100644
index 0000000000..0ea3085286
--- /dev/null
+++ b/Units/parser-cxx.r/template-specializations-including-op.d/expected.tags
@@ -0,0 +1,8 @@
+Point	input.cpp	/^struct Point {$/;"	s	file:
+distance	input.cpp	/^  int distance(void) {$/;"	f	struct:Point	typeref:typename:int	file:
+NS	input.cpp	/^namespace NS {$/;"	n	file:
+MyReal	input.cpp	/^  using MyReal = float;$/;"	t	namespace:NS	typeref:typename:float	file:
+MyVec	input.cpp	/^  using MyVec = T[2];$/;"	t	namespace:NS	typeref:typename:T[2]	file:
+distance	input.cpp	/^int Point<int>::distance(void) { return 1; }$/;"	f	class:Point	typeref:typename:int
+distance	input.cpp	/^int Point<NS::MyReal>::distance(void) { return 1; }$/;"	f	class:Point	typeref:typename:int
+distance	input.cpp	/^int Point<NS::MyVec<int>>::distance(void) { return 1; }$/;"	f	class:Point	typeref:typename:int
diff --git a/Units/parser-cxx.r/template-specializations-including-op.d/input.cpp b/Units/parser-cxx.r/template-specializations-including-op.d/input.cpp
new file mode 100644
index 0000000000..7752ef75d5
--- /dev/null
+++ b/Units/parser-cxx.r/template-specializations-including-op.d/input.cpp
@@ -0,0 +1,21 @@
+template <class T>
+struct Point {
+  int distance(void) {
+    return 0;
+  }
+};
+
+namespace NS {
+  using MyReal = float;
+  template <class T>
+  using MyVec = T[2];
+};
+
+template<>
+int Point<int>::distance(void) { return 1; }
+
+template<>
+int Point<NS::MyReal>::distance(void) { return 1; }
+
+template<>
+int Point<NS::MyVec<int>>::distance(void) { return 1; }
diff --git a/Units/parser-cxx.r/template-specializations-including-op.d/validator b/Units/parser-cxx.r/template-specializations-including-op.d/validator
new file mode 100644
index 0000000000..30c863ebde
--- /dev/null
+++ b/Units/parser-cxx.r/template-specializations-including-op.d/validator
@@ -0,0 +1 @@
+cxx11
diff --git a/parsers/cxx/cxx_parser_function.c b/parsers/cxx/cxx_parser_function.c
index d8126019f3..ccbb872bd7 100644
--- a/parsers/cxx/cxx_parser_function.c
+++ b/parsers/cxx/cxx_parser_function.c
@@ -1591,10 +1591,37 @@ int cxxParserEmitFunctionTags(
 			{
 				CXXToken * pScopeId = pInfo->pScopeStart;
 
-				pInfo->pScopeStart = cxxTokenChainNextTokenOfType(
+				while (1)
+				{
+					pInfo->pScopeStart = cxxTokenChainNextTokenOfType(
 						pInfo->pScopeStart,
-						CXXTokenTypeMultipleColons
-					);
+						CXXTokenTypeMultipleColons|CXXTokenTypeSmallerThanSign);
+
+					CXX_DEBUG_ASSERT(pInfo->pScopeStart,
+									 "We could find neither '::' nor '<'");
+					if (!pInfo->pScopeStart)
+					{
+						pInfo->pScopeStart = pInfo->pIdentifierStart;
+						break;
+					}
+
+					if (cxxTokenTypeIs(pInfo->pScopeStart, CXXTokenTypeMultipleColons))
+						break;	// Good!
+
+					if (cxxTokenTypeIs(pInfo->pScopeStart, CXXTokenTypeSmallerThanSign))
+					{
+						// Skip the template arguments.
+						// Should we add the template arguments to the scope? (FIXME)
+						pInfo->pScopeStart = cxxTokenChainSkipToEndOfTemplateAngleBracket(pInfo->pScopeStart);
+						CXX_DEBUG_ASSERT(pInfo->pScopeStart,
+										 "We could not find '>', the end of template argument(s)");
+						if (!pInfo->pScopeStart)
+						{
+							pInfo->pScopeStart = pInfo->pIdentifierStart;
+							break;
+						}
+					}
+				}
 
 				CXX_DEBUG_ASSERT(pInfo->pScopeStart,"We should have found a next token here");