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 desulfurized in a first hydrodesulfurization stage. The effluent stream from this first stage is sent to a separation zone wherein a lower boiling naphtha stream and a higher boiling naphtha stream are produced. The lower boiling naphtha stream is sent through at least two more separation zones, each at a lower temperature than the preceding separation stage. The higher boiling naphtha stream, which contains most of the sulfur moieties, is passed to a second hydrodesulfurization stage wherein at least a fraction of the sulfur moieties are removed.