Andredakis et al. (cite{r3}) fit Sersic's law mu (r) ~ r1/n to the bulges of the Balcells & Peletier (cite{r5}) galaxy sample, and infer that n drops with morphological type T from n ~ 4-6 for S0 to n=1 (exponential) for Sc's. We use collisionless N body simulations to test the assumption that initially the surface brightness profiles of all bulges were exponential, and that the steepening of the profiles toward the early-types is due to satellite accretion. The results are positive. After the accretion of a satellite, bulge-disk fits show that the bulge grows and that the bulge profile index n increases proportional to the satellite mass. For a satellite as massive as the bulge, n rises from 1 to 4. We present kinematic diagnostics on the remnants and disk thickening. The latter suggests that the bulge growth must have occurred before the last formation of a thin disk in the galaxy. The thick disks created by the merger are reminiscent of thick disks seen in early-type edge-on galaxies. The efficiency of the process suggests that present day bulges of late-type spirals showing exponential profiles cannot have grown significantly by collisionless mergers.