Naphtha hydrodesulfurization selectivity is increased by reducing the amount of COX (CO plus ½ CO2) in the hydrodesulfurization reaction zone to less than 100 vppm. While this is useful for non-selective hydrodesulfurization, it is particularly useful for selectively desulfurizing an olefin-containing naphtha without octane loss due to olefin saturation by hydrogenation. The COX reduction is achieved by removing COX from the treat gas before it is passed into the reaction zone.