A process for reducing the sulfur content of a hydrocarbon stream is disclosed. A full range cracked naphtha is contacted with a hydrogenation catalyst to convert at least a portion of the dienes and mercaptans to thioethers and to hydrogenate at least a portion of the dienes. The full range cracked naphtha is fractionated into a light naphtha fraction, a medium naphtha fraction, and a heavy naphtha fraction. The heavy naphtha fraction is hydrodesulfurized. The medium naphtha fraction is mixed with hydrogen and gas oil to form a mixture, which is contacted with a hydrodesulfurization catalyst to produce a medium naphtha fraction having a reduced sulfur concentration. The light, heavy, and medium naphtha fractions may then be recombined to form a hydrodesulfurized product having a sulfur content of less than 10 ppm in some embodiments.