diff --git a/lib/tokenize.cpp b/lib/tokenize.cpp
index 6f9cf90a852..69c937cfb30 100644
--- a/lib/tokenize.cpp
+++ b/lib/tokenize.cpp
@@ -5725,8 +5725,6 @@ bool Tokenizer::simplifyTokenList1(const char FileName[])
 
     simplifyFunctionTryCatch();
 
-    simplifyHeadersAndUnusedTemplates();
-
     // Remove __asm..
     simplifyAsm();
 
@@ -5754,6 +5752,8 @@ bool Tokenizer::simplifyTokenList1(const char FileName[])
     // remove __attribute__((?))
     simplifyAttribute();
 
+    simplifyHeadersAndUnusedTemplates();
+
     validate();
 
     // Bail out if code is garbage
@@ -6518,7 +6518,7 @@ void Tokenizer::simplifyHeadersAndUnusedTemplates()
             }
         }
 
-        if (!tok->previous() || Token::Match(tok->previous(), "[;{}]")) {
+        if (!tok->previous() || Token::Match(tok->previous(), "[;{}:]")) {
             // Remove unused function declarations
             if (isIncluded && removeUnusedIncludedFunctions) {
                 while (true) {
@@ -6551,7 +6551,7 @@ void Tokenizer::simplifyHeadersAndUnusedTemplates()
 
             if (removeUnusedTemplates || (isIncluded && removeUnusedIncludedTemplates)) {
                 if (Token::Match(tok, "template < %name%")) {
-                    const Token *closingBracket = tok->next()->findClosingBracket();
+                    Token *closingBracket = tok->next()->findClosingBracket();
                     if (Token::Match(closingBracket, "> class|struct %name% [;:{]") && keep.find(closingBracket->strAt(2)) == keep.end()) {
                         const Token *endToken = closingBracket->tokAt(3);
                         if (endToken->str() == ":") {
@@ -6565,11 +6565,58 @@ void Tokenizer::simplifyHeadersAndUnusedTemplates()
                             Token::eraseTokens(tok, endToken);
                             tok->deleteThis();
                         }
-                    } else if (Token::Match(closingBracket, "> %type% %name% (") && Token::simpleMatch(closingBracket->linkAt(3), ") {") && keep.find(closingBracket->strAt(2)) == keep.end()) {
-                        const Token *endToken = closingBracket->linkAt(3)->linkAt(1)->next();
-                        Token::eraseTokens(tok, endToken);
-                        tok->deleteThis();
-                        goBack = true;
+                    } else {
+                        Token *funcTok = closingBracket->next();
+                        while (funcTok) {
+                            if (Token::Match(funcTok, "::|constexpr|static|inline|const|%type%|&|&&|*") && !Token::Match(funcTok, "%name% (")) {
+                                funcTok = funcTok->next();
+                                continue;
+                            }
+                            if (Token::simpleMatch(funcTok, "<")) {
+                                funcTok = funcTok->findClosingBracket();
+                                if (funcTok) {
+                                    funcTok = funcTok->next();
+                                } else {
+                                    break;
+                                }
+                                continue;
+                            }
+                            break;
+                        }
+                        if (!funcTok)
+                            break;
+                        if (!Token::Match(funcTok, "%name% (")) {
+                            tok = funcTok;
+                            continue;
+                        }
+                        funcTok = funcTok->linkAt(1);
+                        if (funcTok) {
+                            funcTok = funcTok->next();
+                        }
+                        while (funcTok) {
+                            if (Token::Match(funcTok, "throw|noexcept (")) {
+                                funcTok = funcTok->linkAt(1);
+                                if (funcTok) {
+                                    funcTok = funcTok->next();
+                                }
+                                continue;
+                            }
+                            if (Token::Match(funcTok, "const|volatile|&|&&")) {
+                                funcTok = funcTok->next();
+                                continue;
+                            }
+                            break;
+                        }
+                        if (!Token::simpleMatch(funcTok, "{")) {
+                            tok = funcTok;
+                            continue;
+                        }
+                        funcTok = funcTok->link();
+                        if (funcTok) {
+                            Token::eraseTokens(tok, funcTok->next());
+                            tok->deleteThis();
+                            goBack = true;
+                        }
                     }
                 }
             }
diff --git a/test/cli/other_test.py b/test/cli/other_test.py
index 243f600b5a6..7a848b04960 100644
--- a/test/cli/other_test.py
+++ b/test/cli/other_test.py
@@ -3415,6 +3415,76 @@ def test_check_unused_templates_func(tmp_path):  # #13714
     (void)(*((int*)0));
 }
 
+class S {
+public:
+    template<typename T>
+    void f_t_3()
+    {
+        (void)(*((int*)0));
+    }
+}
+
+template<typename T>
+static inline void f_t_4()
+{
+    (void)(*((int*)0));
+}
+
+template<typename T>
+const void *f_t_5()
+{
+    (void)(*((int*)0));
+}
+
+template<typename T>
+void f_t_6() __attribute__((noreturn))
+{
+    (void)(*((int*)0));
+}
+
+template<typename T>
+__attribute__((noreturn)) void f_t_7()
+{
+    (void)(*((int*)0));
+}
+
+template<typename T>
+__declspec(noreturn) void f_t_8()
+{
+    (void)(*((int*)0));
+}
+
+template<typename T>
+[[noreturn]] void f_t_9()
+{
+    (void)(*((int*)0));
+}
+
+template<typename T>
+void f_t_10() noexcept(true)
+{
+    (void)(*((int*)0));
+}
+
+template<typename T>
+void f_t_11() throw(true)
+{
+    (void)(*((int*)0));
+}
+
+struct S {
+    template<typename T>
+    void f_t_12() const {
+        (void)(*((int*)0));
+    }
+};
+
+template<typename T>
+std::vector<T> f_t_13() {
+    (void)(*((int*)0));
+    return {};
+}
+
 void f() {}
 """)