Computational methods are used to analyze bidding in first price sealed bid auctions for a broad range of realistic scenarios. Bidders valuations may have both common value and firm-specific components, and the accuracy of their estimates of the common value component may differ. In addition, we allow for a subset of “naive” bidders, defined as bidders who do not account for the Winners’ Curse. Following Rothkopf (1969, 1980), Wilson (1984), and Compte and Postlewaite (2012), we obtain a constant Shading Factor that maximizes ex-ante expected profits. Our computations show that profit-maximizing shading is greatly impacted by asymmetries in the bidding population and, in particular, by the presence of naive bidders. Failing to account for the presence of naive bidders results in underbidding only in one case, when facing a single rival who is naive, and in overbidding in all other cases. Overbidding is particularly severe when the population of naive competitors is large.