diff --git a/Lib/test/test_urllib2net.py b/Lib/test/test_urllib2net.py
index 8b9435a..a4af01a 100644
--- a/Lib/test/test_urllib2net.py
+++ b/Lib/test/test_urllib2net.py
@@ -156,6 +156,18 @@
         self.assertEqual(res.geturl(),
                 "http://docs.python.org/glossary.html")
 
+    def test_custom_headers(self):
+        url = "http://www.example.com"
+        opener = urllib.request.build_opener()
+        request = urllib.request.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/urllib/request.py b/Lib/urllib/request.py
index 16d8125..6c6450f 100644
--- a/Lib/urllib/request.py
+++ b/Lib/urllib/request.py
@@ -1063,8 +1063,10 @@
             raise URLError('no host given')
 
         h = http_class(host, timeout=req.timeout) # will parse host:port
-        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))
 
         # TODO(jhylton): Should this be redesigned to handle
         # persistent connections?