A process for the selective hydrodesulfurization of olefinic naphtha streams containing a substantial amount of organically bound sulfur and olefins. The olefinic naphtha stream is selectively hydrodesulfurized in a first sulfur removal stage and resulting product stream, which contains hydrogen sulfide and organosulfur is fractionated at a temperature to produce a light fraction containing less than about 100 wppm organically bound sulfur and a heavy fraction containing greater than about 100 wppm organically bound sulfur. The light fraction is stripped of at least a portion ofits hydrogen sulfide and can be collected or passed to gasoline blending. The heavy fraction is passed to a second sulfur removal stage wherein at least a portion of any remaining organically bound sulfur is removed.