diff --git a/stdlib/3/concurrent/futures/_base.pyi b/stdlib/3/concurrent/futures/_base.pyi
index 00ef5b6c3..547d68e7a 100644
--- a/stdlib/3/concurrent/futures/_base.pyi
+++ b/stdlib/3/concurrent/futures/_base.pyi
@@ -1,9 +1,9 @@
 from typing import TypeVar, Generic, Any, Iterable, Iterator, Callable, Tuple, Optional, Set
 from collections import namedtuple
 
-FIRST_COMPLETED = ...  # type: Any
-FIRST_EXCEPTION = ...  # type: Any
-ALL_COMPLETED = ...  # type: Any
+FIRST_COMPLETED = ...  # type: str
+FIRST_EXCEPTION = ...  # type: str
+ALL_COMPLETED = ...  # type: str
 PENDING = ...  # type: Any
 RUNNING = ...  # type: Any
 CANCELLED = ...  # type: Any
@@ -27,14 +27,14 @@ class Future(Generic[_T]):
     def done(self) -> bool: ...
     def add_done_callback(self, fn: Callable[[Future], Any]) -> None: ...
     def result(self, timeout: Optional[float] = ...) -> _T: ...
-    def exception(self, timeout: Optional[float] = ...) -> BaseException: ...
+    def exception(self, timeout: Optional[float] = ...) -> Optional[BaseException]: ...
     def set_running_or_notify_cancel(self) -> None: ...
     def set_result(self, result: _T) -> None: ...
-    def set_exception(self, exception: BaseException) -> None: ...
+    def set_exception(self, exception: Optional[BaseException]) -> None: ...
 
 class Executor:
     def submit(self, fn: Callable[..., _T], *args: Any, **kwargs: Any) -> Future[_T]: ...
-    def map(self, func: Callable[..., _T], *iterables: Any, timeout: Optional[float] = ..., chunksize: int = ...) -> Iterable[_T]: ...
+    def map(self, func: Callable[..., _T], *iterables: Iterable[Any], timeout: Optional[float] = ..., chunksize: int = ...) -> Iterator[_T]: ...
     def shutdown(self, wait: bool = ...) -> None: ...
     def __enter__(self) -> Executor: ...
     def __exit__(self, exc_type: Any, exc_val: Any, exc_tb: Any) -> bool: ...
diff --git a/stdlib/3/concurrent/futures/process.pyi b/stdlib/3/concurrent/futures/process.pyi
index b157d2b33..8076c2d05 100644
--- a/stdlib/3/concurrent/futures/process.pyi
+++ b/stdlib/3/concurrent/futures/process.pyi
@@ -1,14 +1,9 @@
-from typing import Any, Callable, TypeVar, Iterable, Optional
+from typing import Optional, Any
 from ._base import Future, Executor
 
 EXTRA_QUEUED_CALLS = ...  # type: Any
 
 class BrokenProcessPool(RuntimeError): ...
 
-_T = TypeVar('_T')
-
 class ProcessPoolExecutor(Executor):
     def __init__(self, max_workers: Optional[int] = ...) -> None: ...
-    def submit(self, fn: Callable[..., _T], *args: Any, **kwargs: Any) -> Future[_T]: ...
-    def map(self, func: Callable[..., _T], *iterables: Any, timeout: Optional[float] = ..., chunksize: int = ...) -> Iterable[_T]: ...
-    def shutdown(self, wait: bool = ...) -> None: ...
diff --git a/stdlib/3/concurrent/futures/thread.pyi b/stdlib/3/concurrent/futures/thread.pyi
index e366d4d3a..1774b639c 100644
--- a/stdlib/3/concurrent/futures/thread.pyi
+++ b/stdlib/3/concurrent/futures/thread.pyi
@@ -1,10 +1,5 @@
-from typing import Any, TypeVar, Callable, Iterable, Optional
+from typing import Optional
 from ._base import Executor, Future
 
-_T = TypeVar('_T')
-
 class ThreadPoolExecutor(Executor):
     def __init__(self, max_workers: Optional[int] = ...) -> None: ...
-    def submit(self, fn: Callable[..., _T], *args: Any, **kwargs: Any) -> Future[_T]: ...
-    def map(self, func: Callable[..., _T], *iterables: Any, timeout: Optional[float] = ..., chunksize: int = ...) -> Iterable[_T]: ...
-    def shutdown(self, wait: bool = ...) -> None: ...
diff --git a/third_party/2/concurrent/futures/__init__.pyi b/third_party/2/concurrent/futures/__init__.pyi
index 02c11a2a6..4604830ed 100644
--- a/third_party/2/concurrent/futures/__init__.pyi
+++ b/third_party/2/concurrent/futures/__init__.pyi
@@ -26,16 +26,16 @@ class Future(Generic[_T]):
 
 class Executor:
     def submit(self, fn: Callable[..., _T], *args: Any, **kwargs: Any) -> Future[_T]: ...
-    def map(self, func: Callable[..., _T], *iterables: Any, timeout: Optional[float] = ...) -> Iterable[_T]: ...
+    def map(self, func: Callable[..., _T], *iterables: Iterable[Any], timeout: Optional[float] = ...) -> Iterator[_T]: ...
     def shutdown(self, wait: bool = ...) -> None: ...
     def __enter__(self) -> Executor: ...
     def __exit__(self, exc_type: Any, exc_val: Any, exc_tb: Any) -> bool: ...
 
 class ThreadPoolExecutor(Executor):
-    def __init__(self, max_workers: int) -> None: ...
+    def __init__(self, max_workers: Optional[int] = ...) -> None: ...
 
 class ProcessPoolExecutor(Executor):
-    def __init__(self, max_workers: Union[int, None] = ...) -> None: ...
+    def __init__(self, max_workers: Optional[int] = ...) -> None: ...
 
 def wait(fs: Iterable[Future], timeout: Optional[float] = ..., return_when: str = ...) -> Tuple[Set[Future], Set[Future]]: ...