diff --git a/stdlib/3/fileinput.pyi b/stdlib/3/fileinput.pyi
index 3f0179216..7d68c2797 100644
--- a/stdlib/3/fileinput.pyi
+++ b/stdlib/3/fileinput.pyi
@@ -1,16 +1,13 @@
-from typing import Iterable, Callable, IO, AnyStr, Generic, Any, TypeVar
-
-StrOrIterableStr = TypeVar('StrOrIterableStr', str, Iterable[str])
+from typing import Iterable, Callable, IO, AnyStr, Generic, Any, Union, Iterator
 
 
 def input(
-    files: StrOrIterableStr=None,
+    files: Union[str, Iterable[str]]=None,
     inplace: bool=...,
     backup: str=...,
     bufsize: int=...,
     mode: str=...,
-    openhook: Callable[[str, str], IO[AnyStr]]=...
-    ): ...
+    openhook: Callable[[str, str], IO[AnyStr]]=...) -> Iterable[AnyStr]: ...
 
 
 def close() -> None: ...
@@ -23,7 +20,7 @@ def isstdin() -> bool: ...
 class FileInput(Iterable[AnyStr], Generic[AnyStr]):
     def __init__(
         self,
-        files: StrOrIterableStr=None,
+        files: Union[str, Iterable[str]]=None,
         inplace: bool=...,
         backup: str=...,
         bufsize: int=...,
@@ -33,13 +30,13 @@ class FileInput(Iterable[AnyStr], Generic[AnyStr]):
 
     def __del__(self) -> None: ...
     def close(self) -> None: ...
-    def __enter__(self): ...
+    def __enter__(self) -> 'FileInput[AnyStr]': ...
     def __exit__(self, type: Any, value: Any, traceback: Any) -> None: ...
-    def __iter__(self): ...
-    def __next__(self) -> str: ...
-    def __getitem__(self, i) -> str: ...
+    def __iter__(self) -> Iterator[AnyStr]: ...
+    def __next__(self) -> AnyStr: ...
+    def __getitem__(self, i) -> AnyStr: ...
     def nextfile(self) -> None: ...
-    def readline(self) -> str: ...
+    def readline(self) -> AnyStr: ...
     def filename(self) -> str: ...
     def lineno(self) -> int: ...
     def filelineno(self) -> int: ...