diff --git a/stdlib/2/__builtin__.pyi b/stdlib/2/__builtin__.pyi
index 5c203e1ec..490c15b14 100644
--- a/stdlib/2/__builtin__.pyi
+++ b/stdlib/2/__builtin__.pyi
@@ -1356,11 +1356,17 @@ else:
             *iterables: Iterable[Any]) -> List[_S]: ...
 if sys.version_info >= (3,):
     @overload
-    def max(__arg1: _T, __arg2: _T, *_args: _T, key: Callable[[_T], Any] = ...) -> _T: ...
+    def max(__arg1: _LT, __arg2: _LT, *_args: _LT, key: None = ...) -> _LT: ...
     @overload
-    def max(__iterable: Iterable[_T], *, key: Callable[[_T], Any] = ...) -> _T: ...
+    def max(__arg1: _T, __arg2: _T, *_args: _T, key: Callable[[_T], _LT]) -> _T: ...
     @overload
-    def max(__iterable: Iterable[_T], *, key: Callable[[_T], Any] = ..., default: _VT) -> Union[_T, _VT]: ...
+    def max(__iterable: Iterable[_LT], *, key: None = ...) -> _LT: ...
+    @overload
+    def max(__iterable: Iterable[_T], *, key: Callable[[_T], _LT]) -> _T: ...
+    @overload
+    def max(__iterable: Iterable[_LT], *, key: None = ..., default: _T) -> Union[_LT, _T]: ...
+    @overload
+    def max(__iterable: Iterable[_T1], *, key: Callable[[_T1], _LT], default: _T2) -> Union[_T1, _T2]: ...
 else:
     @overload
     def max(__arg1: _T, __arg2: _T, *_args: _T, key: Callable[[_T], Any] = ...) -> _T: ...
@@ -1368,11 +1374,17 @@ else:
     def max(__iterable: Iterable[_T], *, key: Callable[[_T], Any] = ...) -> _T: ...
 if sys.version_info >= (3,):
     @overload
-    def min(__arg1: _T, __arg2: _T, *_args: _T, key: Callable[[_T], Any] = ...) -> _T: ...
+    def min(__arg1: _LT, __arg2: _LT, *_args: _LT, key: None = ...) -> _LT: ...
     @overload
-    def min(__iterable: Iterable[_T], *, key: Callable[[_T], Any] = ...) -> _T: ...
+    def min(__arg1: _T, __arg2: _T, *_args: _T, key: Callable[[_T], _LT]) -> _T: ...
     @overload
-    def min(__iterable: Iterable[_T], *, key: Callable[[_T], Any] = ..., default: _VT) -> Union[_T, _VT]: ...
+    def min(__iterable: Iterable[_LT], *, key: None = ...) -> _LT: ...
+    @overload
+    def min(__iterable: Iterable[_T], *, key: Callable[[_T], _LT]) -> _T: ...
+    @overload
+    def min(__iterable: Iterable[_LT], *, key: None = ..., default: _T) -> Union[_LT, _T]: ...
+    @overload
+    def min(__iterable: Iterable[_T1], *, key: Callable[[_T1], _LT], default: _T2) -> Union[_T1, _T2]: ...
 else:
     @overload
     def min(__arg1: _T, __arg2: _T, *_args: _T, key: Callable[[_T], Any] = ...) -> _T: ...
diff --git a/stdlib/2and3/builtins.pyi b/stdlib/2and3/builtins.pyi
index 5c203e1ec..490c15b14 100644
--- a/stdlib/2and3/builtins.pyi
+++ b/stdlib/2and3/builtins.pyi
@@ -1356,11 +1356,17 @@ else:
             *iterables: Iterable[Any]) -> List[_S]: ...
 if sys.version_info >= (3,):
     @overload
-    def max(__arg1: _T, __arg2: _T, *_args: _T, key: Callable[[_T], Any] = ...) -> _T: ...
+    def max(__arg1: _LT, __arg2: _LT, *_args: _LT, key: None = ...) -> _LT: ...
     @overload
-    def max(__iterable: Iterable[_T], *, key: Callable[[_T], Any] = ...) -> _T: ...
+    def max(__arg1: _T, __arg2: _T, *_args: _T, key: Callable[[_T], _LT]) -> _T: ...
     @overload
-    def max(__iterable: Iterable[_T], *, key: Callable[[_T], Any] = ..., default: _VT) -> Union[_T, _VT]: ...
+    def max(__iterable: Iterable[_LT], *, key: None = ...) -> _LT: ...
+    @overload
+    def max(__iterable: Iterable[_T], *, key: Callable[[_T], _LT]) -> _T: ...
+    @overload
+    def max(__iterable: Iterable[_LT], *, key: None = ..., default: _T) -> Union[_LT, _T]: ...
+    @overload
+    def max(__iterable: Iterable[_T1], *, key: Callable[[_T1], _LT], default: _T2) -> Union[_T1, _T2]: ...
 else:
     @overload
     def max(__arg1: _T, __arg2: _T, *_args: _T, key: Callable[[_T], Any] = ...) -> _T: ...
@@ -1368,11 +1374,17 @@ else:
     def max(__iterable: Iterable[_T], *, key: Callable[[_T], Any] = ...) -> _T: ...
 if sys.version_info >= (3,):
     @overload
-    def min(__arg1: _T, __arg2: _T, *_args: _T, key: Callable[[_T], Any] = ...) -> _T: ...
+    def min(__arg1: _LT, __arg2: _LT, *_args: _LT, key: None = ...) -> _LT: ...
     @overload
-    def min(__iterable: Iterable[_T], *, key: Callable[[_T], Any] = ...) -> _T: ...
+    def min(__arg1: _T, __arg2: _T, *_args: _T, key: Callable[[_T], _LT]) -> _T: ...
     @overload
-    def min(__iterable: Iterable[_T], *, key: Callable[[_T], Any] = ..., default: _VT) -> Union[_T, _VT]: ...
+    def min(__iterable: Iterable[_LT], *, key: None = ...) -> _LT: ...
+    @overload
+    def min(__iterable: Iterable[_T], *, key: Callable[[_T], _LT]) -> _T: ...
+    @overload
+    def min(__iterable: Iterable[_LT], *, key: None = ..., default: _T) -> Union[_LT, _T]: ...
+    @overload
+    def min(__iterable: Iterable[_T1], *, key: Callable[[_T1], _LT], default: _T2) -> Union[_T1, _T2]: ...
 else:
     @overload
     def min(__arg1: _T, __arg2: _T, *_args: _T, key: Callable[[_T], Any] = ...) -> _T: ...