diff --git a/stdlib/2and3/fractions.pyi b/stdlib/2and3/fractions.pyi
index 66408fbff..90771a63a 100644
--- a/stdlib/2and3/fractions.pyi
+++ b/stdlib/2and3/fractions.pyi
@@ -30,11 +30,11 @@ class Fraction(Rational):
                  *,
                  _normalize: bool = True) -> None: ...
     @overload
-    def __init__(self, value: float, *, _normalize=True) -> None: ...
+    def __init__(self, value: float, *, _normalize: bool = True) -> None: ...
     @overload
-    def __init__(self, value: Decimal, *, _normalize=True) -> None: ...
+    def __init__(self, value: Decimal, *, _normalize: bool = True) -> None: ...
     @overload
-    def __init__(self, value: str, *, _normalize=True) -> None: ...
+    def __init__(self, value: str, *, _normalize: bool = True) -> None: ...
 
     @classmethod
     def from_float(cls, f: float) -> 'Fraction': ...
diff --git a/stdlib/3.4/asyncio/locks.pyi b/stdlib/3.4/asyncio/locks.pyi
index d80ddc424..559effd98 100644
--- a/stdlib/3.4/asyncio/locks.pyi
+++ b/stdlib/3.4/asyncio/locks.pyi
@@ -1,4 +1,4 @@
-from typing import Any, Callable, Generator, Iterable, Iterator, TypeVar, Union
+from typing import Any, Callable, Generator, Iterable, Iterator, TypeVar, Union, Optional
 
 from .coroutines import coroutine
 from .events import AbstractEventLoop
@@ -49,11 +49,11 @@ class Condition(_ContextManagerMixin):
     def notify_all(self) -> None: ...
 
 class Semaphore(_ContextManagerMixin):
-    def __init__(self, value: int = 1, *, loop: AbstractEventLoop = None) -> None: ...
+    def __init__(self, value: int = ..., *, loop: Optional[AbstractEventLoop] = ...) -> None: ...
     def locked(self) -> bool: ...
     @coroutine
     def acquire(self) -> Generator[Any, None, bool]: ...
     def release(self) -> None: ...
 
 class BoundedSemaphore(Semaphore):
-    def __init__(self, value=1, *, loop: AbstractEventLoop = None) -> None: ...
+    def __init__(self, value: int = ..., *, loop: Optional[AbstractEventLoop] = ...) -> None: ...
diff --git a/stdlib/3.4/asyncio/tasks.pyi b/stdlib/3.4/asyncio/tasks.pyi
index e95d758ae..bf69df8ea 100644
--- a/stdlib/3.4/asyncio/tasks.pyi
+++ b/stdlib/3.4/asyncio/tasks.pyi
@@ -15,7 +15,7 @@ FIRST_COMPLETED = 'FIRST_COMPLETED'
 ALL_COMPLETED = 'ALL_COMPLETED'
 
 def as_completed(fs: Sequence[_FutureT[_T]], *, loop: AbstractEventLoop = ...,
-                 timeout=None) -> Iterator[Generator[Any, None, _T]]: ...
+                 timeout: Optional[float] = ...) -> Iterator[Generator[Any, None, _T]]: ...
 def ensure_future(coro_or_future: _FutureT[_T],
                   *, loop: AbstractEventLoop = ...) -> Future[_T]: ...
 # TODO: gather() should use variadic type vars instead of _TAny.
diff --git a/stdlib/3/_posixsubprocess.pyi b/stdlib/3/_posixsubprocess.pyi
index a048a10c8..67b7d7cc5 100644
--- a/stdlib/3/_posixsubprocess.pyi
+++ b/stdlib/3/_posixsubprocess.pyi
@@ -2,12 +2,13 @@
 
 # NOTE: These are incomplete!
 
-from typing import Tuple, Sequence
+from typing import Tuple, Sequence, Callable
 
 def cloexec_pipe() -> Tuple[int, int]: ...
 def fork_exec(args: Sequence[str],
-              executable_list, close_fds, fds_to_keep, cwd: str, env_list,
+              executable_list: Sequence[bytes], close_fds: bool, fds_to_keep: Sequence[int],
+              cwd: str, env_list: Sequence[bytes],
               p2cread: int, p2cwrite: int, c2pred: int, c2pwrite: int,
               errread: int, errwrite: int, errpipe_read: int,
-              errpipe_write: int, restore_signals, start_new_session,
-              preexec_fn) -> int: ...
+              errpipe_write: int, restore_signals: int, start_new_session: int,
+              preexec_fn: Callable[[], None]) -> int: ...
diff --git a/stdlib/3/http/client.pyi b/stdlib/3/http/client.pyi
index e59497160..340f09033 100644
--- a/stdlib/3/http/client.pyi
+++ b/stdlib/3/http/client.pyi
@@ -7,6 +7,7 @@ from typing import (
 )
 import email.message
 import io
+from socket import socket
 import sys
 import ssl
 import types
@@ -87,7 +88,7 @@ if sys.version_info >= (3, 5):
         closed = ...  # type: bool
         status = ...  # type: int
         reason = ...  # type: str
-        def __init__(self, sock, debuglevel: int = ...,
+        def __init__(self, sock: socket, debuglevel: int = ...,
                      method: Optional[str] = ..., url: Optional[str] = ...) -> None: ...
         def read(self, amt: Optional[int] = ...) -> bytes: ...
         def readinto(self, b: bytearray) -> int: ...
diff --git a/stdlib/3/shlex.pyi b/stdlib/3/shlex.pyi
index db99fc668..ed23d5aa3 100644
--- a/stdlib/3/shlex.pyi
+++ b/stdlib/3/shlex.pyi
@@ -2,7 +2,7 @@
 
 # Based on http://docs.python.org/3.2/library/shlex.html
 
-from typing import List, Tuple, Any, TextIO
+from typing import List, Tuple, Any, TextIO, Union, Optional
 
 def split(s: str, comments: bool = ...,
           posix: bool = ...) -> List[str]: ...
@@ -26,7 +26,7 @@ class shlex:
     token = ...  # type: str
     eof = ...  # type: str
 
-    def __init__(self, instream=..., infile=...,
+    def __init__(self, instream: Union[str, TextIO] = ..., infile: Optional[str] = ...,
                  posix: bool = ...) -> None: ...
     def get_token(self) -> str: ...
     def push_token(self, tok: str) -> None: ...