In an effort to produce scratch- and damage-free flat surfaces, two non-conventional polishing techniques, mechano-chemical and float, were recently introduced by Yasunaga et al. and Namba and Tsuwa, respectively. The emphasis in both these techniques is on employing an abrasive whose hardness is less than that of the workpiece. This paper describes the results of our efforts to apply these techniques to tape-cast alumina, hot-pressed Si₃N₄, sapphire and single crystals of silicon and gallium arsenide. Samples of polished materials were observed to be scratch free, and in the case of single crystals, very smooth with a peak-to-peak roughness of ≤ 40Å. The polished surfaces have been characterized using several techniques, including reflection high-energy electron diffraction (RHEED), interferometry, profilometry, electron spectroscopy for chemical analysis and Auger electron spectroscopy.