This invention is a method of purifying fuel streams containing organonitrogen and organosulfur impurities. The fuel stream is first treated to extract organonitrogen impurities so that the nitrogen content of the fuel stream is reduced by at least 50 percent. After separation and recovery of the nitrogen-depleted fuel stream, the organosulfur impurities in the fuel stream are then oxidized with an organic hydroperoxide in the presence of a titanium-containing silicon oxide catalyst. The resulting sulfones may be more readily removed from the fuel stream than the non-oxidized organosulfur impurities.