diff --git a/stdlib/3/functools.pyi b/stdlib/3/functools.pyi
index b4295c476..be88c2870 100644
--- a/stdlib/3/functools.pyi
+++ b/stdlib/3/functools.pyi
@@ -1,11 +1,5 @@
-# Stubs for functools (Python 3)
-
-# NOTE: These are incomplete!
-
-from abc import ABCMeta, abstractmethod
 import sys
-from typing import Any, Callable, Generic, Dict, Iterable, Mapping, Optional, Sequence, Tuple, TypeVar, NamedTuple, overload
-from collections import namedtuple
+from typing import Any, Callable, Generic, Dict, Iterable, Mapping, Optional, Sequence, Tuple, Type, TypeVar, NamedTuple, Union, overload
 
 _AnyCallable = Callable[..., Any]
 
@@ -19,15 +13,17 @@ def reduce(function: Callable[[_T, _T], _T],
            sequence: Iterable[_T]) -> _T: ...
 
 
-class CacheInfo(NamedTuple('CacheInfo', [
-    ('hits', int), ('misses', int), ('maxsize', int), ('currsize', int)])
-):
-    ...
+class _CacheInfo(NamedTuple('CacheInfo', [
+    ('hits', int),
+    ('misses', int),
+    ('maxsize', int),
+    ('currsize', int)
+])): ...
 
 class _lru_cache_wrapper(Generic[_T]):
     __wrapped__ = ...  # type: Callable[..., _T]
     def __call__(self, *args: Any, **kwargs: Any) -> _T: ...
-    def cache_info(self) -> CacheInfo: ...
+    def cache_info(self) -> _CacheInfo: ...
 
 class lru_cache():
     def __init__(self, maxsize: Optional[int] = ..., typed: bool = ...) -> None: ...
@@ -51,6 +47,22 @@ class partial(Generic[_T]):
     def __call__(self, *args: Any, **kwargs: Any) -> _T: ...
 
 if sys.version_info >= (3, 4):
+    # With protocols, this could change into a generic protocol that defines __get__ and returns _T
+    _Descriptor = Any
+
+    class partialmethod(Generic[_T]):
+        func: Union[Callable[..., _T], _Descriptor]
+        args: Tuple[Any, ...]
+        keywords: Dict[str, Any]
+
+        @overload
+        def __init__(self, func: Callable[..., _T], *args: Any, **keywords: Any) -> None: ...
+        @overload
+        def __init__(self, func: _Descriptor, *args: Any, **keywords: Any) -> None: ...
+        def __get__(self, obj: Any, cls: Type[Any]) -> Callable[..., _T]: ...
+        @property
+        def __isabstractmethod__(self) -> bool: ...
+
     class _SingleDispatchCallable(Generic[_T]):
         registry = ...  # type: Mapping[Any, Callable[..., _T]]
         def dispatch(self, cls: Any) -> Callable[..., _T]: ...