Drops impacting superhydrophobic surfaces normally spread, retract, and leave the surface in an approximately spherical shape, with little loss of energy. Recently, however, it was shown that drops can leave the substrate before retracting while still in an extended pancake-like form. We use mesoscale simulations and theoretical arguments, compared to experimental data, to show that such "pancake bouncing" occurs when impacting fluid that enters the surface is slowed and then expelled by capillary forces. For the drop to bounce as a pancake, two criteria must be satisfied: the fluid must return to the surface at the appropriate time, and it must do so with sufficient kinetic energy to lift the drop. We argue that this will occur for superhydrophobic surfaces with topological features having dimensions of similar to 200 rho m, larger than those normally considered. The contact time of pancake bouncing events is reduced by up to 5-fold compared to that of conventional bouncing, suggesting relevance to drop shedding and anti-icing applications.