In sponsored search auctions advertisers typically pay a fixed amount per click that their advertisements receive. In particular, the advertiser and the publisher enter into a contract (e.g., the publisher displays the ad; the advertiser pays the publisher 10 cents per click), and each party’s subjective value for such a contract depends on their estimated click-through rates (CTR) for the ad. Starting from this motivating example, we define and analyze a class of contract auctions that generalize the classical second price auction. As an application, we introduce impression-plus-click pricing for sponsored search, in which advertisers pay a fixed amount per impression plus an additional amount if their ad is clicked. Of note, when the advertiser’s estimated CTR is higher than the publisher’s estimated CTR, both parties find negative click payments advantageous, where the advertiser pays the publisher a premium for the impression but the publisher then pays the advertiser per click.