diff --git a/M2Crypto/SSL/Connection.py b/M2Crypto/SSL/Connection.py
index 7053aa6..6503935 100644
--- a/M2Crypto/SSL/Connection.py
+++ b/M2Crypto/SSL/Connection.py
@@ -12,6 +12,7 @@ Copyright 2008 Heikki Toivonen. All rights reserved.
 
 import logging
 import socket
+import io
 
 from M2Crypto import BIO, Err, X509, m2, py27plus, six, util  # noqa
 from M2Crypto.SSL import Checker, Context, timeout  # noqa
@@ -584,7 +585,10 @@ class Connection(object):
     def makefile(self, mode='rb', bufsize=-1):
         # type: (AnyStr, int) -> socket._fileobject
         if six.PY3:
-            return socket.SocketIO(self, mode)
+            raw = socket.SocketIO(self, mode)
+            if 'rw' in mode:
+                return io.BufferedRWPair(raw, raw)
+            return io.BufferedReader(raw, io.DEFAULT_BUFFER_SIZE)
         else:
             return socket._fileobject(self, mode, bufsize)