The dynamics of mergers between two unequal elliptical systems was studied with self-consistent numerical simulations. Comparisons of these models to real ellipticals are made in a variety of properties, which include the mean central surface brightness, the shape of the surface brightness profile, and the type of rotation curve and dispersion profile. Several proofs are given that the cores of smaller, denser ellipticals sink to the remnant's center virtually undisturbed, and create a core-within-a-core structure with definite signatures in the surface brightness profile and the velocity dispersion profile. Ellipticals with anomalous cores appear to be a natural outcome of this type of merger.