This invention is a method of purifying fuel streams containing organosulfur impurities. The fuel stream is oxidized with an organic hydroperoxide in the presence of an oxidation catalyst to form a sulfone product. The alcohol product of the organic hydroperoxide is then removed from the oxidized fuel stream, followed by extraction of the sulfone product by solid-liquid extraction using solid adsorbents. The alcohol removal step is found to improve the adsorption capacity of the solid adsorbents.