When potential bidders for a target firm are heterogeneous, standard auction methods for selling the firm are not optimal, as they treat the bidders symmetrically. In a two-bidder contest, one way to discriminate against the stronger bidder is to impose an order of moves. A simple “matching auction” can achieve this objective, in which the “strong” bidder is asked to make a first and final offer, and the other bidder is asked to match this bid. We consider two sources of bidder heterogeneity in a common-value setting: differences in initial toeholds, and asymmetric effects of the bidders' private signals on value. The matching auction results in a higher expected selling price than the standard auctions when the asymmetry is sufficiently large. Other properties of the matching auction are discussed.