We show that asymmetry in bidders' capacity constraints plays an important role in inhibiting collusion and promoting competitive outcomes in multi-unit discriminatory and uniform-price auctions. This effect seems to be related to the increased difficulty of coordination when there are fundamental differences between bidders. Asymmetry in capacity constraints plays a more important role under the discriminatory price mechanism, and leads to a reversal of the revenue ranking in a study with an identical experimental design, but where bidders have symmetric capacity constraints (SSZ (2004)). These results suggest that the optimal auction format may depend on factors specific to a particular auction setting.