diff --git a/Lib/smtplib.py b/Lib/smtplib.py
--- a/Lib/smtplib.py
+++ b/Lib/smtplib.py
@@ -614,7 +614,7 @@
             if not _have_ssl:
                 raise RuntimeError("No SSL support included in this Python")
             self.sock = ssl.wrap_socket(self.sock, keyfile, certfile)
-            self.file = SSLFakeFile(self.sock)
+            self.file = self.sock.makefile('rb')
             # RFC 3207:
             # The client MUST discard any knowledge obtained from
             # the server, such as the list of SMTP service extensions,
@@ -754,7 +754,7 @@
             if self.debuglevel > 0: print>>stderr, 'connect:', (host, port)
             sock = socket.create_connection((host, port), timeout)
             sock = ssl.wrap_socket(sock, self.keyfile, self.certfile)
-            self.file = SSLFakeFile(self.sock)
+            self.file = sock.makefile('rb')
             return sock
 
     __all__.append("SMTP_SSL")