Processes for the desulfurization of a cracked naphtha by the reaction of hydrogen with the organic sulfur compounds present in the feed are disclosed. In particular, processes disclosed herein may use one or more catalytic distillation steps followed by further hydrodesulfurization of the naphtha in a fixed bed reactor. It has been found that the formation of recombinant mercaptans in the fixed bed reactor effluent may be reduced or eliminated by reducing the concentration of hydrogen sulfide and/or olefins at the exit of the fixed bed reactor. The reduction or elimination in the formation of recombinant mercaptans may be accomplished by recycling a select portion of the fixed bed reactor effluent to the fixed bed reactor, where the select portion has a relatively low or nil concentration of olefins. Processes disclosed herein may thus facilitate the production of hydrodesulfurized cracked naphthas having a total sulfur content of less than 10 ppm, by weight.