The welfare impact of a merger involves the market power offense and the efficiency defense. Salant et al. (1983) show that mergers among symmetric firms are unprofitable except for monopolization. We characterize the limit to this merger paradox in a simple linear Cournot oligopoly with asymmetric costs. Farrell and Shapiro (1990) provide sufficient conditions for a profitable merger to increase welfare but leave open whether it exists. We characterize the degree of cost asymmetry making a merger both profitable and socially desirable. Comparing rationalization and synergy within the efficiency defense, we show that for most industry structures, a rationalization merger is more likely to be welfare enhancing but a synergy merger is more likely to be profitable.