diff --git a/stdlib/2.7/functools.pyi b/stdlib/2.7/functools.pyi
index 32a299f91..62f593747 100644
--- a/stdlib/2.7/functools.pyi
+++ b/stdlib/2.7/functools.pyi
@@ -1,6 +1,6 @@
 # Stubs for functools (Python 2.7)
-#
-# NOTE: This dynamically typed stub was automatically generated by stubgen.
+
+# NOTE: These are incomplete!
 
 from abc import ABCMeta, abstractmethod
 from typing import Any, Callable, Generic, Dict, Iterator, Optional, Sequence, Tuple, TypeVar
@@ -12,6 +12,10 @@ _T = TypeVar("_T")
 def reduce(function: Callable[[_T], _T],
            sequence: Iterator[_T], initial: Optional[_T] = ...) -> _T: ...
 
+# TODO implement as class; more precise typing
+# TODO cache_info and __wrapped__ attributes
+def lru_cache(maxsize: Optional[int] = ...) -> Callable[[Any], Any]: ...
+
 WRAPPER_ASSIGNMENTS = ... # type: Sequence[str]
 WRAPPER_UPDATES = ... # type: Sequence[str]
 
diff --git a/stdlib/3/functools.pyi b/stdlib/3/functools.pyi
index 93d258eb6..06a3637f2 100644
--- a/stdlib/3/functools.pyi
+++ b/stdlib/3/functools.pyi
@@ -1,12 +1,33 @@
-# Stubs for functools
+# Stubs for functools (Python 3)
 
 # NOTE: These are incomplete!
 
-from typing import Callable, Any, Optional
+from abc import ABCMeta, abstractmethod
+from typing import Any, Callable, Generic, Dict, Iterator, Optional, Sequence, Tuple, TypeVar
+from collections import namedtuple
+
+_AnyCallable = Callable[..., Any]
+
+_T = TypeVar("_T")
+def reduce(function: Callable[[_T], _T],
+           sequence: Iterator[_T], initial: Optional[_T] = ...) -> _T: ...
 
 # TODO implement as class; more precise typing
 # TODO cache_info and __wrapped__ attributes
 def lru_cache(maxsize: Optional[int] = ...) -> Callable[[Any], Any]: ...
 
-# TODO more precise typing?
-def wraps(func: Any) -> Any: ...
+WRAPPER_ASSIGNMENTS = ... # type: Sequence[str]
+WRAPPER_UPDATES = ... # type: Sequence[str]
+
+def update_wrapper(wrapper: _AnyCallable, wrapped: _AnyCallable, assigned: Sequence[str] = ...,
+                   updated: Sequence[str] = ...) -> None: ...
+def wraps(wrapped: _AnyCallable, assigned: Sequence[str] = ..., updated: Sequence[str] = ...) -> Callable[[_AnyCallable], _AnyCallable]: ...
+def total_ordering(cls: type) -> type: ...
+def cmp_to_key(mycmp: Callable[[_T, _T], bool]) -> Callable[[_T], Any]: ...
+
+class partial(Generic[_T]):
+    func = ...  # Callable[..., _T]
+    args = ...  # type: Tuple[Any, ...]
+    keywords = ...  # type: Dict[str, Any]
+    def __init__(self, func: Callable[..., _T], *args: Any, **kwargs: Any) -> None: ...
+    def __call__(self, *args: Any, **kwargs: Any) -> _T: ...