diff --git a/stdlib/2/__builtin__.pyi b/stdlib/2/__builtin__.pyi
index 541122b27..33b25f56d 100644
--- a/stdlib/2/__builtin__.pyi
+++ b/stdlib/2/__builtin__.pyi
@@ -574,9 +574,11 @@ class dict(MutableMapping[_KT, _VT], Generic[_KT, _VT]):
     def popitem(self) -> Tuple[_KT, _VT]: ...
     def setdefault(self, k: _KT, default: _VT = ...) -> _VT: ...
     @overload
-    def update(self, m: Mapping[_KT, _VT], **kwargs: _VT) -> None: ...
+    def update(self, __m: Mapping[_KT, _VT], **kwargs: _VT) -> None: ...
     @overload
-    def update(self, m: Iterable[Tuple[_KT, _VT]], **kwargs: _VT) -> None: ...
+    def update(self, __m: Iterable[Tuple[_KT, _VT]], **kwargs: _VT) -> None: ...
+    @overload
+    def update(self, **kwargs: _VT) -> None: ...
     def iterkeys(self) -> Iterator[_KT]: ...
     def itervalues(self) -> Iterator[_VT]: ...
     def iteritems(self) -> Iterator[Tuple[_KT, _VT]]: ...
diff --git a/stdlib/2/collections.pyi b/stdlib/2/collections.pyi
index 4a56ea5a4..1fab27443 100644
--- a/stdlib/2/collections.pyi
+++ b/stdlib/2/collections.pyi
@@ -78,9 +78,11 @@ class Counter(Dict[_T, int], Generic[_T]):
     # Dict.update. Not sure if we should use '# type: ignore' instead
     # and omit the type from the union.
     @overload
-    def update(self, m: Mapping[_T, int], **kwargs: int) -> None: ...
+    def update(self, __m: Mapping[_T, int], **kwargs: int) -> None: ...
     @overload
-    def update(self, m: Union[Iterable[_T], Iterable[Tuple[_T, int]]], **kwargs: int) -> None: ...
+    def update(self, __m: Union[Iterable[_T], Iterable[Tuple[_T, int]]], **kwargs: int) -> None: ...
+    @overload
+    def update(self, **kwargs: int) -> None: ...
 
     def __add__(self, other: Counter[_T]) -> Counter[_T]: ...
     def __sub__(self, other: Counter[_T]) -> Counter[_T]: ...
diff --git a/stdlib/2/typing.pyi b/stdlib/2/typing.pyi
index 73497f9aa..0fef6d4a1 100644
--- a/stdlib/2/typing.pyi
+++ b/stdlib/2/typing.pyi
@@ -238,9 +238,11 @@ class MutableMapping(Mapping[_KT, _VT], Generic[_KT, _VT]):
     def popitem(self) -> Tuple[_KT, _VT]: ...
     def setdefault(self, k: _KT, default: _VT = ...) -> _VT: ...
     @overload
-    def update(self, m: Mapping[_KT, _VT], **kwargs: _VT) -> None: ...
+    def update(self, __m: Mapping[_KT, _VT], **kwargs: _VT) -> None: ...
     @overload
-    def update(self, m: Iterable[Tuple[_KT, _VT]], **kwargs: _VT) -> None: ...
+    def update(self, __m: Iterable[Tuple[_KT, _VT]], **kwargs: _VT) -> None: ...
+    @overload
+    def update(self, **kwargs: _VT) -> None: ...
 
 Text = unicode
 
diff --git a/stdlib/3/builtins.pyi b/stdlib/3/builtins.pyi
index f2a3b1b92..8ccd0363c 100644
--- a/stdlib/3/builtins.pyi
+++ b/stdlib/3/builtins.pyi
@@ -635,9 +635,11 @@ class dict(MutableMapping[_KT, _VT], Generic[_KT, _VT]):
     def popitem(self) -> Tuple[_KT, _VT]: ...
     def setdefault(self, k: _KT, default: _VT = None) -> _VT: ...
     @overload
-    def update(self, m: Mapping[_KT, _VT], **kwargs: _VT) -> None: ...
+    def update(self, __m: Mapping[_KT, _VT], **kwargs: _VT) -> None: ...
     @overload
-    def update(self, m: Iterable[Tuple[_KT, _VT]], **kwargs: _VT) -> None: ...
+    def update(self, __m: Iterable[Tuple[_KT, _VT]], **kwargs: _VT) -> None: ...
+    @overload
+    def update(self, **kwargs: _VT) -> None: ...
     def keys(self) -> KeysView[_KT]: ...
     def values(self) -> ValuesView[_VT]: ...
     def items(self) -> ItemsView[_KT, _VT]: ...
diff --git a/stdlib/3/collections/__init__.pyi b/stdlib/3/collections/__init__.pyi
index e31bbf7b6..e10d86183 100644
--- a/stdlib/3/collections/__init__.pyi
+++ b/stdlib/3/collections/__init__.pyi
@@ -138,9 +138,11 @@ class Counter(Dict[_T, int], Generic[_T]):
     # Dict.update. Not sure if we should use '# type: ignore' instead
     # and omit the type from the union.
     @overload
-    def update(self, m: Mapping[_T, int], **kwargs: int) -> None: ...
+    def update(self, __m: Mapping[_T, int], **kwargs: int) -> None: ...
     @overload
-    def update(self, m: Union[Iterable[_T], Iterable[Tuple[_T, int]]], **kwargs: int) -> None: ...
+    def update(self, __m: Union[Iterable[_T], Iterable[Tuple[_T, int]]], **kwargs: int) -> None: ...
+    @overload
+    def update(self, **kwargs: int) -> None: ...
 
     def __add__(self, other: Counter[_T]) -> Counter[_T]: ...
     def __sub__(self, other: Counter[_T]) -> Counter[_T]: ...
diff --git a/stdlib/3/typing.pyi b/stdlib/3/typing.pyi
index cb2a2c92a..a7899a4a2 100644
--- a/stdlib/3/typing.pyi
+++ b/stdlib/3/typing.pyi
@@ -327,9 +327,11 @@ class MutableMapping(Mapping[_KT, _VT], Generic[_KT, _VT]):
     # known to be a Mapping with unknown type parameters, which is closer
     # to the behavior we want. See mypy issue  #1430.
     @overload
-    def update(self, m: Mapping[_KT, _VT], **kwargs: _VT) -> None: ...
+    def update(self, __m: Mapping[_KT, _VT], **kwargs: _VT) -> None: ...
     @overload
-    def update(self, m: Iterable[Tuple[_KT, _VT]], **kwargs: _VT) -> None: ...
+    def update(self, __m: Iterable[Tuple[_KT, _VT]], **kwargs: _VT) -> None: ...
+    @overload
+    def update(self, **kwargs: _VT) -> None: ...
 
 Text = str