A method is described for reducing the sulfur content in a hydrocarbon stream. Cracked naphtha full fraction is brought into contact with a hydrogenation catalyst to convert at least part of the dienes and mercaptans to thioethers and to hydrogenate at least part of the dienes. Full-fraction cracked naphtha is divided into a light naphtha fraction, a middle naphtha fraction, and a heavy naphtha fraction. The heavy naphtha fraction is hydrodesulphurized. The middle fraction of naphtha is mixed with hydrogen and gas oil to form a mixture, which is brought into contact with a hydrodesulfurization catalyst, to obtain an average fraction of naphtha having a lower sulfur concentration. In some embodiments, the light, heavy, and medium naphtha fractions can then be recombined to form a hydrodesulfurized product having a sulfur content of less than 10 ppm.
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