diff --git a/CHANGES.md b/CHANGES.md
index 4eda950fd..0270c0386 100644
--- a/CHANGES.md
+++ b/CHANGES.md
@@ -8,6 +8,10 @@ dev
   https://www.python.org/dev/peps/pep-0563/
   ([PR #400](https://github.com/cloudpipe/cloudpickle/pull/400))
 
+- Stricter parametrized type detection heuristics in
+  _is_parametrized_type_hint to limit false positives.
+  ([PR #409](https://github.com/cloudpipe/cloudpickle/pull/409))
+
 1.6.0
 =====
 
diff --git a/cloudpickle/cloudpickle.py b/cloudpickle/cloudpickle.py
index d1b38f826..20e9a9550 100644
--- a/cloudpickle/cloudpickle.py
+++ b/cloudpickle/cloudpickle.py
@@ -455,15 +455,31 @@ def _extract_class_dict(cls):
 
 if sys.version_info[:2] < (3, 7):  # pragma: no branch
     def _is_parametrized_type_hint(obj):
-        # This is very cheap but might generate false positives.
+        # This is very cheap but might generate false positives. So try to
+        # narrow it down is good as possible.
+        type_module = getattr(type(obj), '__module__', None)
+        from_typing_extensions = type_module == 'typing_extensions'
+        from_typing = type_module == 'typing'
+
         # general typing Constructs
         is_typing = getattr(obj, '__origin__', None) is not None
 
         # typing_extensions.Literal
-        is_literal = getattr(obj, '__values__', None) is not None
+        is_literal = (
+            (getattr(obj, '__values__', None) is not None)
+            and from_typing_extensions
+        )
 
         # typing_extensions.Final
-        is_final = getattr(obj, '__type__', None) is not None
+        is_final = (
+            (getattr(obj, '__type__', None) is not None)
+            and from_typing_extensions
+        )
+
+        # typing.ClassVar
+        is_classvar = (
+            (getattr(obj, '__type__', None) is not None) and from_typing
+        )
 
         # typing.Union/Tuple for old Python 3.5
         is_union = getattr(obj, '__union_params__', None) is not None
@@ -472,8 +488,8 @@ def _is_parametrized_type_hint(obj):
             getattr(obj, '__result__', None) is not None and
             getattr(obj, '__args__', None) is not None
         )
-        return any((is_typing, is_literal, is_final, is_union, is_tuple,
-                    is_callable))
+        return any((is_typing, is_literal, is_final, is_classvar, is_union,
+                    is_tuple, is_callable))
 
     def _create_parametrized_type_hint(origin, args):
         return origin[args]
diff --git a/tests/cloudpickle_test.py b/tests/cloudpickle_test.py
index 4e7eac466..845f27962 100644
--- a/tests/cloudpickle_test.py
+++ b/tests/cloudpickle_test.py
@@ -2301,6 +2301,26 @@ def reduce_myclass(x):
         finally:
             copyreg.dispatch_table.pop(MyClass)
 
+    def test_literal_misdetection(self):
+        # see https://github.com/cloudpipe/cloudpickle/issues/403
+        class MyClass:
+            @property
+            def __values__(self):
+                return ()
+
+        o = MyClass()
+        pickle_depickle(o, protocol=self.protocol)
+
+    def test_final_or_classvar_misdetection(self):
+        # see https://github.com/cloudpipe/cloudpickle/issues/403
+        class MyClass:
+            @property
+            def __type__(self):
+                return int
+
+        o = MyClass()
+        pickle_depickle(o, protocol=self.protocol)
+
 
 class Protocol2CloudPickleTest(CloudPickleTest):