The Nuker law was designed to match the inner few (~3-10) arcseconds of predominantly nearby (<~30 Mpc) early-type galaxy light profiles; it was never intended to describe an entire profile. The Sérsic model, on the other hand, was developed to fit the entire profile; however, because of the presence of partially depleted galaxy cores, the Sérsic model cannot always describe the very inner region. We have therefore developed a new empirical model consisting of an inner power law, a transition region, and an outer Sérsic model to connect the inner and outer structure of elliptical galaxies. We have additionally explored the stability of the Nuker model parameters. Surprisingly, none are found to be stable quantities; all are shown to vary systematically with a profile's fitted radial extent, and often by more than 100%. Considering elliptical galaxies spanning a range of 7.5 mag, we reveal that the central stellar densities of the underlying host galaxies increase with galaxy luminosity until the onset of core formation, detected only in the brightest elliptical galaxies. We suggest that the so-called power-law galaxies may actually be described by the Sérsic model over their entire radial range. Based on observations made with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555.