diff --git a/stdlib/3/functools.pyi b/stdlib/3/functools.pyi
index c24faf811..29866a18c 100644
--- a/stdlib/3/functools.pyi
+++ b/stdlib/3/functools.pyi
@@ -3,7 +3,8 @@
 # NOTE: These are incomplete!
 
 from abc import ABCMeta, abstractmethod
-from typing import Any, Callable, Generic, Dict, Iterable, Optional, Sequence, Tuple, TypeVar, NamedTuple, overload
+import sys
+from typing import Any, Callable, Generic, Dict, Iterable, Mapping, Optional, Sequence, Tuple, TypeVar, NamedTuple, overload
 from collections import namedtuple
 
 _AnyCallable = Callable[..., Any]
@@ -43,8 +44,21 @@ def total_ordering(cls: type) -> type: ...
 def cmp_to_key(mycmp: Callable[[_T, _T], int]) -> Callable[[_T], Any]: ...
 
 class partial(Generic[_T]):
-    func = ...  # Callable[..., _T]
+    func = ...  # type: 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: ...
+
+if sys.version_info >= (3, 4):
+    class _SingleDispatchCallable(Generic[_T]):
+        registry = ...  # type: Mapping[Any, Callable[..., _T]]
+        def dispatch(self, cls: Any) -> Callable[..., _T]: ...
+        @overload
+        def register(self, cls: Any) -> Callable[[Callable[..., _T]], Callable[..., _T]]: ...
+        @overload
+        def register(self, cls: Any, func: Callable[..., _T]) -> Callable[..., _T]: ...
+        def _clear_cache(self) -> None: ...
+        def __call__(self, *args: Any, **kwargs: Any) -> _T: ...
+
+    def singledispatch(func: Callable[..., _T]) -> _SingleDispatchCallable[_T]: ...
diff --git a/third_party/2and3/singledispatch.pyi b/third_party/2and3/singledispatch.pyi
index dac3ceae8..ed24b7f1f 100644
--- a/third_party/2and3/singledispatch.pyi
+++ b/third_party/2and3/singledispatch.pyi
@@ -1,5 +1,17 @@
-# Stubs for singledispatch (Python 3.5)
-#
-# NOTE: This dynamically typed stub was automatically generated by stubgen.
+from typing import Any, Callable, Generic, Mapping, Optional, TypeVar, overload
 
-def singledispatch(func): ...
+
+_T = TypeVar("_T")
+
+
+class _SingleDispatchCallable(Generic[_T]):
+    registry = ...  # type: Mapping[Any, Callable[..., _T]]
+    def dispatch(self, cls: Any) -> Callable[..., _T]: ...
+    @overload
+    def register(self, cls: Any) -> Callable[[Callable[..., _T]], Callable[..., _T]]: ...
+    @overload
+    def register(self, cls: Any, func: Callable[..., _T]) -> Callable[..., _T]: ...
+    def _clear_cache(self) -> None: ...
+    def __call__(self, *args: Any, **kwargs: Any) -> _T: ...
+
+def singledispatch(func: Callable[..., _T]) -> _SingleDispatchCallable[_T]: ...