diff --git a/stdlib/2/itertools.pyi b/stdlib/2/itertools.pyi
index 644d9f1b1..4d9edbc32 100644
--- a/stdlib/2/itertools.pyi
+++ b/stdlib/2/itertools.pyi
@@ -26,9 +26,9 @@ class chain(Iterator[_T], Generic[_T]):
 def compress(data: Iterable[_T], selectors: Iterable[Any]) -> Iterator[_T]: ...
 def dropwhile(predicate: Callable[[_T], Any],
               iterable: Iterable[_T]) -> Iterator[_T]: ...
-def ifilter(predicate: Callable[[_T], Any],
+def ifilter(predicate: Optional[Callable[[_T], Any]],
             iterable: Iterable[_T]) -> Iterator[_T]: ...
-def ifilterfalse(predicate: Callable[[_T], Any],
+def ifilterfalse(predicate: Optional[Callable[[_T], Any]],
                  iterable: Iterable[_T]) -> Iterator[_T]: ...
 
 @overload
diff --git a/stdlib/3/builtins.pyi b/stdlib/3/builtins.pyi
index c283abe1d..f2a3b1b92 100644
--- a/stdlib/3/builtins.pyi
+++ b/stdlib/3/builtins.pyi
@@ -773,7 +773,8 @@ def exec(object: str, globals: Dict[str, Any] = None,
          locals: Mapping[str, Any] = None) -> Any: ...  # TODO code object as source
 def exit(code: Any = ...) -> NoReturn: ...
 @overload
-def filter(function: Callable[[_T], Any], iterable: Iterable[_T]) -> Iterator[_T]: ...
+def filter(function: Optional[Callable[[_T], Any]],
+           iterable: Iterable[_T]) -> Iterator[_T]: ...
 @overload
 def filter(function: None, iterable: Iterable[Optional[_T]]) -> Iterator[_T]: ...
 def format(o: object, format_spec: str = '') -> str: ...
diff --git a/stdlib/3/itertools.pyi b/stdlib/3/itertools.pyi
index 774d68fb3..3e4379a03 100644
--- a/stdlib/3/itertools.pyi
+++ b/stdlib/3/itertools.pyi
@@ -29,7 +29,7 @@ class chain(Iterator[_T], Generic[_T]):
 def compress(data: Iterable[_T], selectors: Iterable[Any]) -> Iterator[_T]: ...
 def dropwhile(predicate: Callable[[_T], Any],
               iterable: Iterable[_T]) -> Iterator[_T]: ...
-def filterfalse(predicate: Callable[[_T], Any],
+def filterfalse(predicate: Optional[Callable[[_T], Any]],
                 iterable: Iterable[_T]) -> Iterator[_T]: ...
 
 @overload