We investigate the nuclear and global structure of early-type galaxies, and the apparent disparity between the Nuker and Sersic models for radial light profiles. We show that the so-called "power-law" galaxies in fact have Sersic r1/n profiles over their entire observed radial range. Consequently, only three (Sersic-profile) parameters are required to simultaneously describe both the inner (HST-resolved) and outer profiles of low-luminosity (M > -20.5 B-mag) elliptical galaxies. We also find that "core galaxies" have Sersic profiles with a (partially evacuated) single power-law core. We have developed a modified (5-parameter) Sersic profile with a power-law core to model the complete radial extent of luminous galaxies with cores. In addition to quantifying the global stellar distribution in these systems, we have derived new estimates of their core radii (and central mass deficits) and compare these with values obtained using the (5-parameter) Nuker model. Support for proposal number HST-AR-09927.01-A was provided by NASA through a grant from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555.