We used HST WFPC2 images to identify six early-type galaxies with surface- brightness profiles that decrease inward over a limited range of radii near their centers. The implied luminosity density profiles of these galaxies have local minima interior to their core break radii. NGC 3706 harbors a high surface brightness ring of starlight with radius ~20 pc. Its central structure may be related to that in the double-nucleus galaxies M31 and NGC 4486B. NGC 4406 and NGC 6876 have nearly flat cores that on close inspection are centrally depressed. Colors for both galaxies imply that this is not due to dust absorption. The surface brightness distributions of both galaxies are consistent with stellar tori that are more diffuse than the sharply defined system in NGC 3706. The remaining three galaxies are the brightest cluster galaxies in A260, A347, and A3574. Color information is not available for these objects, but they strongly resemble NGC 4406 and NGC 6876 in their cores. The thin ring in NGC 3706 may have formed dissipatively. The five other galaxies resemble the endpoints of some simulations of the merging of two gas-free stellar systems, each harboring a massive nuclear black hole. In one version of this scenario, diffuse stellar tori are produced when stars initially bound to one black hole are tidally stripped away by the second black hole. Alternatively, some inward-decreasing surface-brightness profiles may reflect the ejection of stars from a core during the hardening of the binary black hole created during the merger.