I have combined the Emsellem et al. ATLAS3D rotation measures of a large sample of early-type galaxies with Hubble Space Telescope based classifications of their central structure to characterize the rotation velocities of galaxies with cores. "Core galaxies" rotate slowly, while "power-law galaxies" (galaxies that lack cores) rotate rapidly, confirming the analysis of Faber et al. Significantly, the amplitude of rotation sharply discriminates between the two types in the -19 > MV> -22 domain over which the two types coexist. The slow rotation in the small set of core galaxies with MV> -20, in particular, brings them into concordance with the more massive core galaxies. The ATLAS3D "fast-rotating" and "slow-rotating" early-type galaxies are essentially the same as power-law and core galaxies, respectively, or the Kormendy & Bender two families of elliptical galaxies based on rotation, isophote shape, and central structure. The ATLAS3D fast rotators do include roughly half of the core galaxies, but their rotation amplitudes are always at the lower boundary of that subset. Essentially, all core galaxies have ATLAS3D rotation amplitudes λRe/2 ≤ 0.25, while all galaxies with λRe/2 > 0.25 and figure eccentricity >0.2 lack cores. Both figure rotation and the central structure of early-type galaxies should be used together to separate systems that appear to have formed from "wet" versus "dry" mergers.