This paper analyzes the problem of matching two heterogeneous populations, such as men and women. If the payoff from a match exhibits complementarities, it is well known that, absent any friction, positive assortative matching is optimal. Coarse matching refers to a situation in which the populations are sorted into a finite number of classes and then randomly matched within these classes. We derive upper bounds on the fraction of the total efficiency loss of n-class coarse matching, which is proportional to . Our result substantially enlarges the scope of matching problems in which the performance of coarse matching can be assessed.