We simulate the accretion of high-density dwarf galaxies by low-density giant galaxies, using models that contain both power-law central density cusps and central point masses representing supermassive black holes. The final density profiles of the merger remnants are always similar to the initial density profile of the giant galaxy, for two reasons. 1. The density of the dwarf galaxy is reduced by impulsive heating whenever it passes near the black hole of the giant galaxy. 2. The central density of the giant galaxy drops as it absorbs orbital energy from the dwarf galaxy. The presence or absence of a black hole in the dwarf galaxy has little effect on the final density profile. Our results suggest that the accretion of dense satellites need not result in merger remnants with high central densities.