It's been awhile, but I've purchased airline tickets from Priceline many times. In general, they claim that the "Name your own price" tickets are at least 40% off published rates. So, I'd look on their site (or directly at the ailrine websites) for the dates/city combinations you want and find the lowest published rates. Then, start by bidding about half that amount (or more, depending on how truly discounted you're looking for). Be aware, though, that if your price is not accepted, you can't just up the price on the next bid - you have to either adjust your travel dates or airport. Or else wait 7 days and try again. Or log in using a different email address. Usually, if they don't accept your bid, they'll counter-offer, and then you can choose to accept the price or bid again.