diff --git a/stdlib/2/collections.pyi b/stdlib/2/collections.pyi
index bd7420537..b4c94dd77 100644
--- a/stdlib/2/collections.pyi
+++ b/stdlib/2/collections.pyi
@@ -59,6 +59,8 @@ class deque(Sized, Iterable[_T], Reversible[_T], Generic[_T]):
     def __contains__(self, o: _T) -> bool: ...
     def __reversed__(self) -> Iterator[_T]: ...
 
+_CounterT = TypeVar('_CounterT', bound=Counter)
+
 class Counter(Dict[_T, int], Generic[_T]):
     @overload
     def __init__(self, **kwargs: int) -> None: ...
@@ -66,6 +68,7 @@ class Counter(Dict[_T, int], Generic[_T]):
     def __init__(self, mapping: Mapping[_T, int]) -> None: ...
     @overload
     def __init__(self, iterable: Iterable[_T]) -> None: ...
+    def copy(self: _CounterT) -> _CounterT: ...
     def elements(self) -> Iterator[_T]: ...
     def most_common(self, n: Optional[int] = ...) -> List[Tuple[_T, int]]: ...
     @overload
@@ -93,10 +96,14 @@ class Counter(Dict[_T, int], Generic[_T]):
     def __iand__(self, other: Counter[_T]) -> Counter[_T]: ...
     def __ior__(self, other: Counter[_T]) -> Counter[_T]: ...
 
+_OrderedDictT = TypeVar('_OrderedDictT', bound=OrderedDict)
+
 class OrderedDict(Dict[_KT, _VT], Reversible[_KT], Generic[_KT, _VT]):
     def popitem(self, last: bool = ...) -> Tuple[_KT, _VT]: ...
+    def copy(self: _OrderedDictT) -> _OrderedDictT: ...
     def __reversed__(self) -> Iterator[_KT]: ...
-    def __copy__(self) -> OrderedDict[_KT, _VT]: ...
+
+_DefaultDictT = TypeVar('_DefaultDictT', bound=defaultdict)
 
 class defaultdict(Dict[_KT, _VT], Generic[_KT, _VT]):
     default_factory = ...  # type: Callable[[], _VT]
@@ -111,3 +118,4 @@ class defaultdict(Dict[_KT, _VT], Generic[_KT, _VT]):
     def __init__(self, default_factory: Optional[Callable[[], _VT]],
                  iterable: Iterable[Tuple[_KT, _VT]]) -> None: ...
     def __missing__(self, key: _KT) -> _VT: ...
+    def copy(self: _DefaultDictT) -> _DefaultDictT: ...
diff --git a/stdlib/3/collections/__init__.pyi b/stdlib/3/collections/__init__.pyi
index d5e8f346a..88c2c95aa 100644
--- a/stdlib/3/collections/__init__.pyi
+++ b/stdlib/3/collections/__init__.pyi
@@ -236,6 +236,7 @@ class deque(MutableSequence[_T], Generic[_T]):
         def __mul__(self, other: int) -> deque[_T]: ...
         def __imul__(self, other: int) -> None: ...
 
+_CounterT = TypeVar('_CounterT', bound=Counter)
 
 class Counter(Dict[_T, int], Generic[_T]):
     @overload
@@ -244,7 +245,7 @@ class Counter(Dict[_T, int], Generic[_T]):
     def __init__(self, mapping: Mapping[_T, int]) -> None: ...
     @overload
     def __init__(self, iterable: Iterable[_T]) -> None: ...
-
+    def copy(self: _CounterT) -> _CounterT: ...
     def elements(self) -> Iterator[_T]: ...
 
     def most_common(self, n: Optional[int] = ...) -> List[Tuple[_T, int]]: ...
@@ -277,11 +278,15 @@ class Counter(Dict[_T, int], Generic[_T]):
     def __iand__(self, other: Counter[_T]) -> Counter[_T]: ...
     def __ior__(self, other: Counter[_T]) -> Counter[_T]: ...
 
+_OrderedDictT = TypeVar('_OrderedDictT', bound=OrderedDict)
+
 class OrderedDict(Dict[_KT, _VT], Reversible[_KT], Generic[_KT, _VT]):
     def popitem(self, last: bool = ...) -> Tuple[_KT, _VT]: ...
     def move_to_end(self, key: _KT, last: bool = ...) -> None: ...
+    def copy(self: _OrderedDictT) -> _OrderedDictT: ...
     def __reversed__(self) -> Iterator[_KT]: ...
-    def __copy__(self) -> OrderedDict[_KT, _VT]: ...
+
+_DefaultDictT = TypeVar('_DefaultDictT', bound=defaultdict)
 
 class defaultdict(Dict[_KT, _VT], Generic[_KT, _VT]):
     default_factory = ...  # type: Callable[[], _VT]
@@ -296,9 +301,9 @@ class defaultdict(Dict[_KT, _VT], Generic[_KT, _VT]):
     @overload
     def __init__(self, default_factory: Optional[Callable[[], _VT]],
                  iterable: Iterable[Tuple[_KT, _VT]]) -> None: ...
-
     def __missing__(self, key: _KT) -> _VT: ...
     # TODO __reversed__
+    def copy(self: _DefaultDictT) -> _DefaultDictT: ...
 
 if sys.version_info >= (3, 3):
     class ChainMap(MutableMapping[_KT, _VT], Generic[_KT, _VT]):