diff --git a/stdlib/2and3/traceback.pyi b/stdlib/2and3/traceback.pyi
index ff34ad4cd..2b83b5dcb 100644
--- a/stdlib/2and3/traceback.pyi
+++ b/stdlib/2and3/traceback.pyi
@@ -7,7 +7,7 @@ import sys
 _PT = Tuple[str, int, str, Optional[str]]
 
 
-def print_tb(tb: TracebackType, limit: Optional[int] = ...,
+def print_tb(tb: Optional[TracebackType], limit: Optional[int] = ...,
              file: Optional[IO[str]] = ...) -> None: ...
 if sys.version_info >= (3,):
     def print_exception(etype: Type[BaseException], value: BaseException,
@@ -28,7 +28,7 @@ else:
                    file: Optional[IO[str]] = ...) -> None: ...
 def print_stack(f: Optional[FrameType] = ..., limit: Optional[int] = ...,
                 file: Optional[IO[str]] = ...) -> None: ...
-def extract_tb(tb: TracebackType, limit: Optional[int] = ...) -> List[_PT]: ...
+def extract_tb(tb: Optional[TracebackType], limit: Optional[int] = ...) -> List[_PT]: ...
 def extract_stack(f: Optional[FrameType] = ...,
                   limit: Optional[int] = ...) -> List[_PT]: ...
 def format_list(extracted_list: List[_PT]) -> List[str]: ...
@@ -44,14 +44,14 @@ else:
                          tb: TracebackType,
                          limit: Optional[int] = ...) -> List[str]: ...
     def format_exc(limit: Optional[int] = ...) -> str: ...
-def format_tb(tb: TracebackType, limit: Optional[int] = ...) -> List[str]: ...
+def format_tb(tb: Optional[TracebackType], limit: Optional[int] = ...) -> List[str]: ...
 def format_stack(f: Optional[FrameType] = ...,
                  limit: Optional[int] = ...) -> List[str]: ...
 if sys.version_info >= (3, 4):
     def clear_frames(tb: TracebackType) -> None: ...
 if sys.version_info >= (3, 5):
     def walk_stack(f: Optional[FrameType]) -> Iterator[Tuple[FrameType, int]]: ...
-    def walk_tb(tb: TracebackType) -> Iterator[Tuple[FrameType, int]]: ...
+    def walk_tb(tb: Optional[TracebackType]) -> Iterator[Tuple[FrameType, int]]: ...
 if sys.version_info < (3,):
     def tb_lineno(tb: TracebackType) -> int: ...