Now is the ideal time to accumulate loyalty points—good for hotel stays, rental cars and airline tickets. Wise travelers can get two or even three times the points for one reservation, thanks to a fierce battle between travel websites Orbitz, which unveiled a major rising of the customer payback this week, Expedia and Hotels.com. Even infrequent travelers can collect booking-site points on top of airline miles and credit-card paybacks, and sometimes double-dip on hotel points, too. Why the big discount for consumers? Many travelers use online travel agencies to compare prices, but when it comes time to buy, they go directly to the airline or hotel they want. Online travel agencies used to charge booking fees, giving consumers an incentive to buy elsewhere. But they dropped most of their fees several years ago. The bet now is that fat rewards will turn browsers into buyers.