I also use the site to identify low fares. And then go to Travelocity or AmexITN or the airline site to book. Using the knowledge of the fare and rules, AmexITN can help identify the actual flights with that fare basis available for the candidate dates you have in mind. Bit of trial and error.
Hope this link works to ITN
http://www.itn.net/cgi/get?itn/pl/amex_personal/index
Be sure to register as an expert to see the fare basis codes and availability.