diff --git a/stdlib/2/typing.pyi b/stdlib/2/typing.pyi
index bea5ba985..e43495d7e 100644
--- a/stdlib/2/typing.pyi
+++ b/stdlib/2/typing.pyi
@@ -15,6 +15,8 @@ _promote = object()
 class _SpecialForm(object):
     def __getitem__(self, typeargs: Any) -> object: ...
 
+Union: _SpecialForm = ...
+Optional: _SpecialForm = ...
 Tuple: _SpecialForm = ...
 Generic: _SpecialForm = ...
 Protocol: _SpecialForm = ...
@@ -53,20 +55,17 @@ def no_type_check_decorator(decorator: _C) -> _C: ...
 
 # Type aliases and type constructors
 
-class TypeAlias:
+class _Alias:
     # Class for defining generic aliases for library types.
-    def __init__(self, target_type: type) -> None: ...
     def __getitem__(self, typeargs: Any) -> Any: ...
 
-Union = TypeAlias(object)
-Optional = TypeAlias(object)
-List = TypeAlias(object)
-Dict = TypeAlias(object)
-DefaultDict = TypeAlias(object)
-Set = TypeAlias(object)
-FrozenSet = TypeAlias(object)
-Counter = TypeAlias(object)
-Deque = TypeAlias(object)
+List = _Alias()
+Dict = _Alias()
+DefaultDict = _Alias()
+Set = _Alias()
+FrozenSet = _Alias()
+Counter = _Alias()
+Deque = _Alias()
 
 # Predefined type variables.
 AnyStr = TypeVar('AnyStr', str, unicode)
diff --git a/stdlib/3/typing.pyi b/stdlib/3/typing.pyi
index 6c4dcc253..046d0cf42 100644
--- a/stdlib/3/typing.pyi
+++ b/stdlib/3/typing.pyi
@@ -14,8 +14,10 @@ TypeVar = object()
 _promote = object()
 
 class _SpecialForm:
-    def __getitem__(self, typeargs: Any) -> Any: ...
+    def __getitem__(self, typeargs: Any) -> object: ...
 
+Union: _SpecialForm = ...
+Optional: _SpecialForm = ...
 Tuple: _SpecialForm = ...
 Generic: _SpecialForm = ...
 # Protocol is only present in 3.8 and later, but mypy needs it unconditionally
@@ -61,8 +63,6 @@ class _Alias:
     # Class for defining generic aliases for library types.
     def __getitem__(self, typeargs: Any) -> Any: ...
 
-Union = _Alias()
-Optional = _Alias()
 List = _Alias()
 Dict = _Alias()
 DefaultDict = _Alias()