diff --git a/stdlib/2.7/hmac.pyi b/stdlib/2.7/hmac.pyi
deleted file mode 100644
index 65282cd5a..000000000
--- a/stdlib/2.7/hmac.pyi
+++ /dev/null
@@ -1,13 +0,0 @@
-# Stubs for hmac (Python 2)
-
-from typing import Any, AnyStr
-
-class HMAC:
-    def update(self, msg: str) -> None: ...
-    def digest(self) -> str: ...
-    def hexdigest(self) -> str: ...
-    def copy(self) -> HMAC: ...
-
-def new(key: str, msg: str = ..., digestmod: Any = ...) -> HMAC: ...
-
-def compare_digest(a: AnyStr, b: AnyStr) -> bool: ...
diff --git a/stdlib/2and3/hmac.pyi b/stdlib/2and3/hmac.pyi
new file mode 100644
index 000000000..af0cdf4ea
--- /dev/null
+++ b/stdlib/2and3/hmac.pyi
@@ -0,0 +1,36 @@
+# Stubs for hmac
+
+from typing import Any, Callable, Optional, Union, overload
+from types import ModuleType
+import sys
+
+_B = Union[bytes, bytearray]
+
+# TODO more precise type for object of hashlib
+_Hash = Any
+
+if sys.version_info >= (3, 4):
+    def new(key: _B, msg: Optional[_B] = ...,
+            digestmod: Optional[Union[str, Callable[[], _Hash], ModuleType]] = ...) -> HMAC: ...
+else:
+    def new(  # type: ignore
+            key: _B, msg: Optional[_B] = ...,
+            digestmod: Optional[Union[Callable[[], _Hash], ModuleType]] = ...) -> HMAC: ...
+
+class HMAC:
+    if sys.version_info >= (3,):
+        digest_size = ...  # type: int
+    if sys.version_info >= (3, 4):
+        block_size = ...  # type: int
+        name = ...  # type: str
+    def update(self, msg: _B) -> None: ...
+    def digest(self) -> bytes: ...
+    def hexdigest(self) -> str: ...
+    def copy(self) -> HMAC: ...
+
+@overload
+def compare_digest(a: str, b: str) -> bool: ...
+@overload
+def compare_digest(a: bytes, b: bytes) -> bool: ...
+@overload
+def compare_digest(a: bytearray, b: bytearray) -> bool: ...
diff --git a/stdlib/3.4/_operator.pyi b/stdlib/3.4/_operator.pyi
deleted file mode 100644
index bb5e94f4e..000000000
--- a/stdlib/3.4/_operator.pyi
+++ /dev/null
@@ -1,108 +0,0 @@
-"""Stub file for the '_operator' module."""
-# This is an autogenerated file. It serves as a starting point
-# for a more precise manual annotation of this module.
-# Feel free to edit the source below, but remove this header when you do.
-
-from typing import Any, List, Tuple, Dict, Generic
-
-def _compare_digest(a, b) -> bool:
-    raise BufferError()
-    raise TypeError()
-
-def abs(*args, **kwargs) -> Any: ...
-
-def add(*args, **kwargs) -> Any: ...
-
-def and_(*args, **kwargs) -> Any: ...
-
-def concat(*args, **kwargs) -> Any: ...
-
-def contains(*args, **kwargs) -> bool: ...
-
-def countOf(*args, **kwargs) -> int: ...
-
-def delitem(*args, **kwargs) -> None: ...
-
-def eq(*args, **kwargs) -> Any: ...
-
-def floordiv(*args, **kwargs) -> Any: ...
-
-def ge(*args, **kwargs) -> Any: ...
-
-def getitem(*args, **kwargs) -> Any: ...
-
-def gt(*args, **kwargs) -> Any: ...
-
-def iadd(*args, **kwargs) -> Any: ...
-
-def iand(*args, **kwargs) -> Any: ...
-
-def iconcat(*args, **kwargs) -> Any: ...
-
-def ifloordiv(*args, **kwargs) -> Any: ...
-
-def ilshift(*args, **kwargs) -> Any: ...
-
-def imod(*args, **kwargs) -> Any: ...
-
-def imul(*args, **kwargs) -> Any: ...
-
-def index(*args, **kwargs) -> Any: ...
-
-def indexOf(*args, **kwargs) -> int: ...
-
-def inv(*args, **kwargs) -> Any: ...
-
-def invert(*args, **kwargs) -> Any: ...
-
-def ior(*args, **kwargs) -> Any: ...
-
-def ipow(*args, **kwargs) -> Any: ...
-
-def irshift(*args, **kwargs) -> Any: ...
-
-def is_(*args, **kwargs) -> bool: ...
-
-def is_not(*args, **kwargs) -> bool: ...
-
-def isub(*args, **kwargs) -> Any: ...
-
-def itruediv(*args, **kwargs) -> Any: ...
-
-def ixor(*args, **kwargs) -> Any: ...
-
-def le(*args, **kwargs) -> Any: ...
-
-def length_hint(a, *args, **kwargs) -> int: ...
-
-def lshift(*args, **kwargs) -> Any: ...
-
-def lt(*args, **kwargs) -> Any: ...
-
-def mod(*args, **kwargs) -> Any: ...
-
-def mul(*args, **kwargs) -> Any: ...
-
-def ne(*args, **kwargs) -> Any: ...
-
-def neg(*args, **kwargs) -> Any: ...
-
-def not_(*args, **kwargs) -> bool: ...
-
-def or_(*args, **kwargs) -> Any: ...
-
-def pos(*args, **kwargs) -> Any: ...
-
-def pow(*args, **kwargs) -> Any: ...
-
-def rshift(*args, **kwargs) -> Any: ...
-
-def setitem(*args, **kwargs) -> None: ...
-
-def sub(*args, **kwargs) -> Any: ...
-
-def truediv(*args, **kwargs) -> Any: ...
-
-def truth(*args, **kwargs) -> bool: ...
-
-def xor(*args, **kwargs) -> Any: ...
diff --git a/stdlib/3/hmac.pyi b/stdlib/3/hmac.pyi
deleted file mode 100644
index 4c7972bb0..000000000
--- a/stdlib/3/hmac.pyi
+++ /dev/null
@@ -1,27 +0,0 @@
-# Stubs for hmac (Python 3.5)
-#
-# NOTE: This dynamically typed stub was automatically generated by stubgen.
-
-from typing import Any
-from _operator import _compare_digest as compare_digest
-
-trans_5C = ... # type: Any
-trans_36 = ... # type: Any
-digest_size = ... # type: Any
-
-class HMAC:
-    blocksize = ... # type: Any
-    digest_cons = ... # type: Any
-    outer = ... # type: Any
-    inner = ... # type: Any
-    digest_size = ... # type: Any
-    block_size = ... # type: Any
-    def __init__(self, key, msg=None, digestmod=None): ...
-    @property
-    def name(self): ...
-    def update(self, msg): ...
-    def copy(self): ...
-    def digest(self): ...
-    def hexdigest(self): ...
-
-def new(key, msg=None, digestmod=None): ...