The tangled battle between airlines and online booking agents has become even knottier. After Expedia announced in December that it would bury American Airlines fares in its search results, the site has plowed ahead and dropped the carrier from its inventory entirely.

The spat began when American announced that on December 21 it would stop selling flights through Orbitz, which receives a commission from the carrier on every ticket sold. Expedia, in a sign of solidarity with its competitor, pushed American Airlines tickets to the bottom of its search results before cutting off the carrier entirely January 1.

The move could be risky for American, as about one-third of U.S. travelers use third-party sites to book flights. Moreover, the whole debacle makes it even trickier for flyers to accurately compare tickets across carriers and to book cheaper, multi-airline itineraries. Happily, Priceline and Kayak still display American Airlines - plus, our very own Travel Search price comparison tool pulls data from both of those websites, in addition to other smaller booking engines.