A process for smoothing a rough surface on a substrate, such as a diamond or silicon carbide substrate, said rough surface including protruding peak portions separated by valleys, said smoothing comprising (a) depositing a coating on said rough surface so as to adhere to and to fill at least the valleys of said rough surface, (b) mechanically polishing the thus coated rough surface so as to achieve a smooth coated surface, and (c) dry etching the smooth coated surface, such as by PACE, so as to remove the remaining coating and at least protruding peak portions of the substrate so as to achieve a smooth surface on the substrate, wherein in the mechanical polishing step (b) the coating is removed at a rate of reduction of thickness greater than the rate at which the substrate is subject to reduction of thickness by the mechanical polishing, and in the dry etching step (c) the coating and substrate are removed at substantially the same or a similar rate of reduction of thickness, and, if necessary, steps (a), (b) and (c) are repeated, or the coating and substrate are removed in separate, alternate preferential etching steps.