diff --git a/lib/tokenize.cpp b/lib/tokenize.cpp
index de3525972..a95840453 100644
--- a/lib/tokenize.cpp
+++ b/lib/tokenize.cpp
@@ -5018,9 +5018,6 @@ void Tokenizer::dump(std::ostream &out) const
 
 void Tokenizer::simplifyHeaders()
 {
-    // TODO : can we remove anything in headers here? Like unused declarations.
-    // Maybe if --dump is used we want to have _everything_.
-
     if (mSettings->checkHeaders && mSettings->checkUnusedTemplates)
         // Full analysis. All information in the headers are kept.
         return;
@@ -5031,11 +5028,16 @@ void Tokenizer::simplifyHeaders()
     const bool removeUnusedIncludedTemplates = !mSettings->checkUnusedTemplates || !mSettings->checkHeaders;
     const bool removeUnusedTemplates = !mSettings->checkUnusedTemplates;
 
-    // We want to remove selected stuff from the headers but not *everything*.
-    // The intention here is to not damage the analysis of the source file.
-    // You should get all warnings in the source file.
-
-    // TODO: Remove unused types/variables/etc in headers..
+    // checkHeaders:
+    //
+    // If it is true then keep all code in the headers. It's possible
+    // to remove unused types/variables if false positives / false
+    // negatives can be avoided.
+    //
+    // If it is false, then we want to remove selected stuff from the
+    // headers but not *everything*. The intention here is to not damage
+    // the analysis of the source file. You should get all warnings in
+    // the source file. You should not get false positives.
 
     // functions and types to keep
     std::set<std::string> keep;
@@ -5043,7 +5045,7 @@ void Tokenizer::simplifyHeaders()
         if (!tok->isName())
             continue;
 
-        if (checkHeaders && tok->fileIndex() != 0)
+        if (!checkHeaders && tok->fileIndex() != 0)
             continue;
 
         if (Token::Match(tok, "%name% (") && !Token::simpleMatch(tok->linkAt(1), ") {")) {
diff --git a/test/testtokenize.cpp b/test/testtokenize.cpp
index 50632a02e..e145ad033 100644
--- a/test/testtokenize.cpp
+++ b/test/testtokenize.cpp
@@ -505,6 +505,8 @@ private:
         TEST_CASE(unknownMacroBeforeReturn);
 
         TEST_CASE(cppcast);
+
+        TEST_CASE(checkHeader1);
     }
 
     std::string tokenizeAndStringify(const char code[], bool simplify = false, bool expand = true, Settings::PlatformType platform = Settings::Native, const char* filename = "test.cpp", bool cpp11 = true) {
@@ -8601,6 +8603,60 @@ private:
             ASSERT_EQUALS(tok->str() == "(", tok->isCast());
         }
     }
+
+    std::string checkHeaders(const char code[], bool f) {
+        // Clear the error buffer..
+        errout.str("");
+
+        Settings settings;
+        settings.checkHeaders = f;
+
+        // Raw tokens..
+        std::vector<std::string> files(1, "test.cpp");
+        std::istringstream istr(code);
+        const simplecpp::TokenList tokens1(istr, files, files[0]);
+
+        // Preprocess..
+        simplecpp::TokenList tokens2(files);
+        std::map<std::string, simplecpp::TokenList*> filedata;
+        simplecpp::preprocess(tokens2, tokens1, files, filedata, simplecpp::DUI());
+
+        Preprocessor preprocessor(settings0, nullptr);
+        preprocessor.setDirectives(tokens1);
+
+        // Tokenizer..
+        Tokenizer tokenizer(&settings0, this);
+        tokenizer.createTokens(std::move(tokens2));
+        tokenizer.simplifyTokens1("");
+
+        return tokenizer.tokens()->stringifyList();
+    }
+
+    void checkHeader1() {
+        // #9977
+        const char code[] = "# 1 \"test.h\"\n"
+                            "struct A {\n"
+                            "    int a = 1;\n"
+                            "    void f() { g(1); }\n"
+                            "    template <typename T> void g(T x) { a = 2; }\n" // <- template is used and should be kept
+                            "};";
+
+        ASSERT_EQUALS("\n\n##file 1\n"
+                      "1: struct A {\n"
+                      "2: int a ; a = 1 ;\n"
+                      "3: void f ( ) { g<int> ( 1 ) ; }\n"
+                      "4: void g<int> ( int x ) ;\n"
+                      "5: } ; void A :: g<int> ( int x ) { a = 2 ; }\n",
+                      checkHeaders(code, true));
+
+        ASSERT_EQUALS("\n\n##file 1\n"
+                      "1: struct A {\n"
+                      "2: int a ; a = 1 ;\n"
+                      "3: void f ( ) { g<int> ( 1 ) ; }\n"
+                      "4: void g<int> ( int x ) ;\n"
+                      "5: } ; void A :: g<int> ( int x ) { a = 2 ; }\n",
+                      checkHeaders(code, false));
+    }
 };
 
 REGISTER_TEST(TestTokenizer)