What I usually do after checking fares on itasoftware is to go to the airline's own website and book directly. From my experience (somewhat limited), domestic tickets can usually be booked this way without any fare difference (sometimes this requires putting the different segments together yourself with the "multi-stops" option). However, for international tickets, the airline's own website is always higher than itasoftware. What I do in cases like these is to use Orbitz. More often than not, Orbitz can find the same itinerary at exactly the same price plus its booking fees. One piece of advice, though, is that itasoftware does not always have the lowest available fare. Sometimes consolidators can beat it by several hundred dollars (only on international itineraries IME). Good luck.

LAX