diff -r 203407036e46 Lib/smtplib.py
--- a/Lib/smtplib.py	Fri Jun 17 21:10:21 2011 +0200
+++ b/Lib/smtplib.py	Fri Jun 17 23:29:56 2011 +0200
@@ -787,7 +787,14 @@
             self.file.close()
         self.file = None
         if self.sock:
-            self.sock.close()
+            try:
+                self.sock.shutdown(socket.SHUT_RDWR)
+            except socket.error as e:
+                # The server might already have closed the connection
+                if e.errno != errno.ENOTCONN:
+                    raise
+            finally:
+                self.sock.close()
         self.sock = None
 
     def quit(self):
diff -r 203407036e46 Lib/test/mock_socket.py
--- a/Lib/test/mock_socket.py	Fri Jun 17 21:10:21 2011 +0200
+++ b/Lib/test/mock_socket.py	Fri Jun 17 23:29:56 2011 +0200
@@ -7,6 +7,7 @@
 # Mock socket module
 _defaulttimeout = None
 _reply_data = None
+SHUT_RDWR = socket_module.SHUT_RDWR
 
 # This is used to queue up data to be read through socket.makefile, typically
 # *before* the socket object is even created. It is intended to handle a single
@@ -98,6 +99,9 @@
     def getpeername(self):
         return 'peer'
 
+    def shutdown(self, how):
+        pass
+
     def close(self):
         pass