diff --git a/stdlib/2.7/__builtin__.pyi b/stdlib/2.7/__builtin__.pyi
index 1c2c2af6b..e47720477 100644
--- a/stdlib/2.7/__builtin__.pyi
+++ b/stdlib/2.7/__builtin__.pyi
@@ -238,9 +238,9 @@ class unicode(basestring, Sequence[unicode]):
     def rindex(self, sub: unicode, start: int = 0, end: int = 0) -> int: ...
     def rjust(self, width: int, fillchar: unicode = u' ') -> unicode: ...
     def rpartition(self, sep: unicode) -> Tuple[unicode, unicode, unicode]: ...
-    def rsplit(self, sep: unicode = ..., maxsplit: int = ...) -> List[unicode]: ...
+    def rsplit(self, sep: Optional[unicode] = ..., maxsplit: int = ...) -> List[unicode]: ...
     def rstrip(self, chars: unicode = ...) -> unicode: ...
-    def split(self, sep: unicode = ..., maxsplit: int = ...) -> List[unicode]: ...
+    def split(self, sep: Optional[unicode] = ..., maxsplit: int = ...) -> List[unicode]: ...
     def splitlines(self, keepends: bool = ...) -> List[unicode]: ...
     def startswith(self, prefix: Union[unicode, Tuple[unicode, ...]], start: int = 0,
                    end: int = ...) -> bool: ...
@@ -318,7 +318,7 @@ class str(basestring, Sequence[str]):
     @overload
     def rpartition(self, sep: unicode) -> Tuple[unicode, unicode, unicode]: ...
     @overload
-    def rsplit(self, sep: str = ..., maxsplit: int = ...) -> List[str]: ...
+    def rsplit(self, sep: Optional[str] = ..., maxsplit: int = ...) -> List[str]: ...
     @overload
     def rsplit(self, sep: unicode, maxsplit: int = ...) -> List[unicode]: ...
     @overload
@@ -326,7 +326,7 @@ class str(basestring, Sequence[str]):
     @overload
     def rstrip(self, chars: unicode) -> unicode: ...
     @overload
-    def split(self, sep: str = ..., maxsplit: int = ...) -> List[str]: ...
+    def split(self, sep: Optional[str] = ..., maxsplit: int = ...) -> List[str]: ...
     @overload
     def split(self, sep: unicode, maxsplit: int = ...) -> List[unicode]: ...
     def splitlines(self, keepends: bool = ...) -> List[str]: ...
@@ -401,9 +401,9 @@ class bytearray(MutableSequence[int]):
     def rindex(self, sub: str, start: int = 0, end: int = ...) -> int: ...
     def rjust(self, width: int, fillchar: str = ...) -> bytearray: ...
     def rpartition(self, sep: str) -> Tuple[bytearray, bytearray, bytearray]: ...
-    def rsplit(self, sep: str = ..., maxsplit: int = ...) -> List[bytearray]: ...
+    def rsplit(self, sep: Optional[str] = ..., maxsplit: int = ...) -> List[bytearray]: ...
     def rstrip(self, chars: str = ...) -> bytearray: ...
-    def split(self, sep: str = ..., maxsplit: int = ...) -> List[bytearray]: ...
+    def split(self, sep: Optional[str] = ..., maxsplit: int = ...) -> List[bytearray]: ...
     def splitlines(self, keepends: bool = ...) -> List[bytearray]: ...
     def startswith(self, prefix: Union[str, Tuple[str, ...]]) -> bool: ...
     def strip(self, chars: str = ...) -> bytearray: ...
diff --git a/stdlib/2.7/socket.pyi b/stdlib/2.7/socket.pyi
index d99a1279a..c7122880f 100644
--- a/stdlib/2.7/socket.pyi
+++ b/stdlib/2.7/socket.pyi
@@ -278,7 +278,7 @@ class socket:
     proto = 0
 
     def __init__(self, family: int = ..., type: int = ...,
-                 proto: int = ..., fileno: int = ...) -> None: ...
+                 proto: int = ...) -> None: ...
 
     # --- methods ---
     # second tuple item is an address
diff --git a/stdlib/3/socket.pyi b/stdlib/3/socket.pyi
index cd2f3d541..8451cfbc2 100644
--- a/stdlib/3/socket.pyi
+++ b/stdlib/3/socket.pyi
@@ -5,7 +5,7 @@
 # see: http://hg.python.org/cpython/file/3d0686d90f55/Lib/socket.py
 # see: http://nullege.com/codes/search/socket
 
-from typing import Any, Tuple, Union, List, overload
+from typing import Any, Tuple, List, Optional, Union, overload
 
 # ----- variables and constants -----
 
@@ -277,7 +277,7 @@ class socket:
     proto = 0
 
     def __init__(self, family: int = ..., type: int = ...,
-                 proto: int = ..., fileno: int = ...) -> None: ...
+                 proto: int = ..., fileno: Optional[int] = ...) -> None: ...
 
     # --- methods ---
     # second tuple item is an address