Ranking the profitability of the first-price auction (FPA) and the second-price auction (SPA) is of fundamental importance to auction theory. However, the theoretical literature on bidder asymmetry has primarily focused on auctions with two bidders. Here, I consider auctions with several asymmetric bidders. As in the empirical literature, it is assumed that any bidder is either weak or strong. There is no unambiguous revenue ranking in this environment. Indeed, I show that the ranking may depend on both the size of the reserve price and the number of bidders. However, there always exists a range of reserve prices for which the FPA strictly dominates the SPA. Moreover, if the asymmetry is not too large, there exists seller own-use valuations for which the FPA with an optimal reserve price is strictly more profitable than the SPA with an optimal reserve price. The FPA may in fact be both more profitable and more efficient than the SPA when the reserve price is endogenous. These results are founded on the methodological insight that the combination of reserve prices and several bidders may allow the use of mechanism design arguments that are simpler than those required when just two bidders are present.