Modern sponsored search auctions are derived from the Generalized Second Price (GSP) auction. Although the GSP auction is not truthful, results by Edelman, Ostrovsky, and Schwarz (2007) and Varian (2007) give senses in which its outcome is equivalent to that of the truthful and welfare-maximizing VCG mechanism. The first main message of this paper is that these properties are not unique to the GSP auction: there is a large class of payment rules that, when coupled with the rank-by-bid allocation rule, induce sponsored search auctions with comparable guarantees. The second main message is that the GSP auction is “optimally simple”, subject to possessing a welfare-maximizing Nash equilibrium, when the complexity of a payment rule is measured using the dependencies between bids and slot prices.