Pay rock-bottom for fullsize/premium rent-a-cars
Find the best Priceline price for the cheapest grade (e.g. subcompact) rent-a-car on a bidding-info site such as biddingfortravel.com or betterbidding.com . Book this rate on PL. Then upgrade at the rental counter, you will usually be able to get a really nice premium car or SUV for $5-$20 over what you paid for the subcompact.