1. just prior to booking, make sure your cookies are cleared on your pc. i have tried this with a few of the 'normal' web based airlines, and suprisingly returned lower fares.
I haven't seen such behaviour on the two websites I regularly use for checking prices and booking flights. Can you tell me for which websites you've observed this "cookie sensitivity"?
Additional tip:
3. Websites that compare prices from multiple airlines may come up with better deals; especially if you don't mind an extra stop in your flight.