diff --git a/stdlib/2.7/threading.pyi b/stdlib/2.7/threading.pyi
index 6342be725..791fa4dde 100644
--- a/stdlib/2.7/threading.pyi
+++ b/stdlib/2.7/threading.pyi
@@ -43,11 +43,7 @@ def stack_size(size: int = ...) -> None: ...
 class ThreadError(Exception):
     pass
 
-class local(object):
-    # TODO: allows arbitrary parameters...
-    def __getattr__(self, name: str) -> Any: ...
-    def __setattr__(self, name: str, value: Any) -> None: ...
-    def __delattr__(self, name: str) -> None: ...
+class local(Any): ...
 
 class Event(object):
     def is_set(self) -> bool: ...
diff --git a/stdlib/3/threading.pyi b/stdlib/3/threading.pyi
index 16523df16..83f2307ae 100644
--- a/stdlib/3/threading.pyi
+++ b/stdlib/3/threading.pyi
@@ -29,6 +29,8 @@ class Timer(Thread):
                  kwargs: Mapping[str, Any] = ...) -> None: ...
     def cancel(self) -> None : ...
 
+class local(Any): ...
+
 class Event:
     def is_set(self) -> bool: ...
     def set(self) -> None: ...
diff --git a/stdlib/3/types.pyi b/stdlib/3/types.pyi
index fbb58d6bc..5e94ee8dd 100644
--- a/stdlib/3/types.pyi
+++ b/stdlib/3/types.pyi
@@ -67,7 +67,7 @@ class MappingProxyType:
     def __getitem__(self, key: str) -> Any: ...
     def __iter__(self) -> Iterator[str]: ...
     def __len__(self) -> int: ...
-class SimpleNamespace: ...
+class SimpleNamespace(Any): ...
 
 class GeneratorType:
     gi_code = ...  # type: CodeType