Compositions and methods for planarizing or polishing a NiP, glass, ceramic or glass-ceramic surface in the manufacture of a computer memory disk. The polishing compositions described herein comprise (a) a liquid carrier, preferably water; (b) an abrasive; (c) purified clay; and optional additives, such as (d) a chemical accelerator or oxidizing agent; and (e) a complexing or coupling agent capable of chemically or ionically complexing with, or coupling to, the NiP, glass, ceramic, and/or glass-ceramic material removed during the polishing process. The complexing or coupling agent carries away the metal, glass, ceramic and/or glass-ceramic particles removed during polishing, to prevent the separated particles from returning to the surface from which they were removed. Also disclosed are methods of planarizing or polishing a NiP, glass, ceramic and/or glass-ceramic surface comprising contacting the surface with the compositions.