diff --git a/stdlib/3/_winapi.pyi b/stdlib/3/_winapi.pyi
index 18a1ee937..785f09bc3 100644
--- a/stdlib/3/_winapi.pyi
+++ b/stdlib/3/_winapi.pyi
@@ -57,7 +57,7 @@ def ConnectNamedPipe(handle: int, overlapped: Literal[True]) -> Overlapped: ...
 @overload
 def ConnectNamedPipe(handle: int, overlapped: Literal[False] = ...) -> None: ...
 @overload
-def ConnectNamedPipe(handle: int, overlapped: bool) -> Any: ...
+def ConnectNamedPipe(handle: int, overlapped: bool) -> Optional[Overlapped]: ...
 
 def CreateFile(file_name: str, desired_access: int, share_mode: int, security_attributes: int, creation_disposition: int, flags_and_attributes: int, template_file: int) -> int: ...
 def CreateJunction(src_path: str, dest_path: str) -> None: ...
@@ -77,11 +77,12 @@ def GetVersion() -> int: ...
 def OpenProcess(desired_access: int, inherit_handle: bool, process_id: int) -> int: ...
 def PeekNamedPipe(handle: int, size: int = ...) -> Union[Tuple[int, int], Tuple[bytes, int, int]]: ...
 
-# TODO: once literal types are supported, overload with Literal[True/False]
 @overload
-def ReadFile(handle: int, size: int, overlapped: Union[int, bool]) -> Any: ...
+def ReadFile(handle: int, size: int, overlapped: Literal[True]) -> Tuple[Overlapped, int]: ...
 @overload
-def ReadFile(handle: int, size: int) -> Tuple[int, int]: ...
+def ReadFile(handle: int, size: int, overlapped: Literal[False] = ...) -> Tuple[bytes, int]: ...
+@overload
+def ReadFile(handle: int, size: int, overlapped: Union[int, bool]) -> Tuple[Any, int]: ...
 
 def SetNamedPipeHandleState(named_pipe: int, mode: Optional[int], max_collection_count: Optional[int], collect_data_timeout: Optional[int]) -> None: ...
 def TerminateProcess(handle: int, exit_code: int) -> None: ...
@@ -89,11 +90,13 @@ def WaitForMultipleObjects(handle_seq: Sequence[int], wait_flag: bool, milliseco
 def WaitForSingleObject(handle: int, milliseconds: int) -> int: ...
 def WaitNamedPipe(name: str, timeout: int) -> None: ...
 
-# TODO: once literal types are supported, overload with Literal[True/False]
+
 @overload
-def WriteFile(handle: int, buffer: bytes, overlapped: Union[int, bool]) -> Any: ...
+def WriteFile(handle: int, buffer: bytes, overlapped: Literal[True]) -> Tuple[Overlapped, int]: ...
 @overload
-def WriteFile(handle: int, buffer: bytes) -> Tuple[bytes, int]: ...
+def WriteFile(handle: int, buffer: bytes, overlapped: Literal[False]) -> Tuple[int, int]: ...
+@overload
+def WriteFile(handle: int, buffer: bytes, overlapped: Union[int, bool]) -> Tuple[Any, int]: ...
 
 
 class Overlapped: