diff --git a/jedi/inference/compiled/value.py b/jedi/inference/compiled/value.py
index e493750f..7458ae40 100644
--- a/jedi/inference/compiled/value.py
+++ b/jedi/inference/compiled/value.py
@@ -264,6 +264,12 @@ class CompiledObject(Value):
             self.access_handle.execute_operation(other.access_handle, operator)
         )
 
+    def execute_annotation(self):
+        if self.access_handle.get_repr() == 'None':
+            # None as an annotation doesn't need to be executed.
+            return ValueSet([self])
+        return super().execute_annotation()
+
     def negate(self):
         return create_from_access_path(self.inference_state, self.access_handle.negate())
 
diff --git a/jedi/third_party/typeshed b/jedi/third_party/typeshed
index 3319cadf..ff92f09e 160000
--- a/jedi/third_party/typeshed
+++ b/jedi/third_party/typeshed
@@ -1 +1 @@
-Subproject commit 3319cadf85012328f8a12b15da4eecc8de0cf305
+Subproject commit ff92f09efbe9c7d67ca13d30ca56c4afbe13f129
diff --git a/test/completion/pep0484_basic.py b/test/completion/pep0484_basic.py
index ba7cab18..6c89c738 100644
--- a/test/completion/pep0484_basic.py
+++ b/test/completion/pep0484_basic.py
@@ -44,7 +44,7 @@ def return_none() -> None:
     """
     pass
 
-#?
+#? None
 return_none()
 
 
diff --git a/test/completion/pep0484_typing.py b/test/completion/pep0484_typing.py
index ae49d10d..9d2cbd83 100644
--- a/test/completion/pep0484_typing.py
+++ b/test/completion/pep0484_typing.py
@@ -214,7 +214,7 @@ def union(p, q, r, s, t):
     r
     #? int() str() float() dict()
     s
-    #? int()
+    #? int() None
     t
 
 def optional(p):
diff --git a/test/test_api/test_signatures.py b/test/test_api/test_signatures.py
index 7264cee3..8b4044ec 100644
--- a/test/test_api/test_signatures.py
+++ b/test/test_api/test_signatures.py
@@ -71,4 +71,4 @@ def test_param_kind_and_name(code, index, param_code, kind, Script, skip_python2
 
 def test_staticmethod(Script):
     s, = Script('staticmethod(').call_signatures()
-    assert s.to_string() == 'staticmethod(f: Callable)'
+    assert s.to_string() == 'staticmethod(f: Callable[..., Any])'
diff --git a/test/test_inference/test_gradual/test_typeshed.py b/test/test_inference/test_gradual/test_typeshed.py
index 4a30cb51..8b7285de 100644
--- a/test/test_inference/test_gradual/test_typeshed.py
+++ b/test/test_inference/test_gradual/test_typeshed.py
@@ -27,13 +27,13 @@ def test_get_typeshed_directories():
     assert dirs == transform({'stdlib/2and3', 'stdlib/3', 'third_party/2and3', 'third_party/3'})
 
     dirs = get_dirs(PythonVersionInfo(3, 5))
-    assert dirs == transform({'stdlib/2and3', 'stdlib/3', 'stdlib/3.5',
-                              'third_party/2and3', 'third_party/3', 'third_party/3.5'})
+    assert dirs == transform({'stdlib/2and3', 'stdlib/3',
+                              'third_party/2and3', 'third_party/3'})
 
     dirs = get_dirs(PythonVersionInfo(3, 6))
-    assert dirs == transform({'stdlib/2and3', 'stdlib/3', 'stdlib/3.5',
+    assert dirs == transform({'stdlib/2and3', 'stdlib/3',
                               'stdlib/3.6', 'third_party/2and3',
-                              'third_party/3', 'third_party/3.5', 'third_party/3.6'})
+                              'third_party/3', 'third_party/3.6'})
 
 
 def test_get_stub_files():