Search auctions have become a dominant source of revenue generation on the Internet. Such auctions have typically used per-click bidding and pricing. We propose the use of hybrid auctions where an advertiser can make a per-impression as well as a per-click bid, and the auctioneer then chooses one of the two as the pricing mechanism. We assume that the advertiser and the auctioneer both have separate beliefs (called priors) on the click-probability of an advertisement. We first prove that the hybrid auction is truthful, assuming that the advertisers are risk-neutral. We then show that this auction is superior to the existing per-click auction in multiple ways: