diff --git a/Lib/smtplib.py b/Lib/smtplib.py
--- a/Lib/smtplib.py
+++ b/Lib/smtplib.py
@@ -701,6 +701,7 @@
             self.file.close()
         self.file = None
         if self.sock:
+            self.sock.shutdown(socket.SHUT_RDWR)
             self.sock.close()
         self.sock = None
 
@@ -774,6 +775,7 @@
         except socket.error, msg:
             if self.debuglevel > 0: print>>stderr, 'connect fail:', host
             if self.sock:
+                self.sock.shutdown(socket.SHUT_RDWR)
                 self.sock.close()
             self.sock = None
             raise socket.error, msg