Tested on 2.7. The same bug exists:

127.0.0.1 - - [07/Apr/2013 13:17:39] "POST / HTTP/1.1" 200 -
('content-length', '11')
('accept-encoding', 'identity')
('connection', 'close')
('user-agent', 'Python-urllib/2.7')
('host', '127.0.0.1:8000')
('content-type', 'application/x-www-form-urlencoded')

Also, the workaround exists for that issue:
instead of using request.add_header have to use request.add_unredirected_header for the second call.

BTW, the same issue with 'Content-length' header. If use request.add_data the second time when the content length value leaves the same as for first request.

See steps to reproduce in attachments.