Mn(III)AlPO-5 and Cr(VI)AlPO-5 redox (microporous) catalysts are effective, in the presence of dissolved acetylperoxyborate (APB) under mild conditions (333-373 K), and much superior to the titanosilicate, TS-1 (also a single-site heterogeneous catalyst), in the selective oxidation of primary, secondary, benzylic and other unsaturated alcohols, p-cymene, methyl cyclohexene and other speciality organics which are of value in the fine-chemical and pharmaceutical industries.