diff --git a/Lib/test/test_urllib2net.py b/Lib/test/test_urllib2net.py
index 56e952d..5ace162 100644
--- a/Lib/test/test_urllib2net.py
+++ b/Lib/test/test_urllib2net.py
@@ -172,6 +172,18 @@
         finally:
             res.close()
 
+    def test_custom_headers(self):
+        url = "http://www.example.com"
+        opener = urllib2.build_opener()
+        request = urllib2.Request(url)
+        self.assertFalse(request.header_items())
+        opener.open(request)
+        self.assertTrue(request.header_items())
+        self.assertTrue(request.has_header('User-agent'))
+        request.add_header('User-Agent','Test-Agent')
+        opener.open(request)
+        self.assertEqual(request.get_header('User-agent'),'Test-Agent')
+
     def _test_urls(self, urls, handlers, retry=True):
         import time
         import logging
diff --git a/Lib/urllib2.py b/Lib/urllib2.py
index 5c717a4..adc6d8c 100644
--- a/Lib/urllib2.py
+++ b/Lib/urllib2.py
@@ -1127,8 +1127,10 @@
         h = http_class(host, timeout=req.timeout) # will parse host:port
         h.set_debuglevel(self._debuglevel)
 
-        headers = dict(req.headers)
-        headers.update(req.unredirected_hdrs)
+        headers = dict(req.unredirected_hdrs)
+        headers.update(dict((k, v) for k, v in req.headers.items()
+                            if k not in headers))
+
         # We want to make an HTTP/1.1 request, but the addinfourl
         # class isn't prepared to deal with a persistent connection.
         # It will try to read all remaining data from the socket,