Deep desulfurization of hydrocarbon feeds containing undesired organosulfur compounds to produce a hydrocarbon product having low levels of sulfur, i.e., 15 ppmw or less of sulfur, is achieved by flashing the feed at a target cut point temperature to obtain two fractions. A first fraction contains refractory organosulfur compounds, which boil at or above the target cut point temperature. A second fraction boiling below the target cut point temperature is substantially free of refractory sulfur-containing compounds. The second fraction is contacted with a hydrodesulfurization catalyst in a hydrodesulfurization reaction zone operating under mild conditions to reduce the quantity of organosulfur compounds to an ultra-low level. The first fraction is contacted with an oxidizing agent and an active metal catalyst in an oxidation reaction zone to convert the refractory organosulfur compounds to oxidized organosulfur compounds. The oxidized organosulfur compounds are removed, producing a stream containing an ultra-low level of organosulfur compounds. The two streams can be combined to obtain a full range hydrocarbon product having an ultra-low level of organosulfur compounds.