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We provide a new set of tools for studying asymmetric .rst price auctions, connecting behaviour of equilibria to the _-concavity of the underlying distributions over costs or values, and showing how one can use surplus expressions related to symmetric auctions to bound behaviour in asymmetric auctions. We apply these tools to studying procurement auctions in which, as is common in practice, one seller is given an advantage, re.ecting, for example, better reliability or quality. We show conditions under which for any given .rst price handicap auction, there is a second price auction with bonuses that outperforms it, with most of our results involving ex-post dominance.