A process for hydrodesulfurizing an olefinic naphtha feedstock while retaining a substantial amount of the olefins, which feedstock has a T95 boiling point below 250° C. and contains at least 50 ppmw of organically bound sulfur and from 5% to 60% olefins, the process including hydrodesulfurizing the feedstock in a sulfur removal stage in the presence of a gas including hydrogen and a hydrodesulfurization catalyst, at hydrodesulfurization reaction conditions, to convert at least 60% of the organically bound sulfur to hydrogen sulfide and to produce a desulfurized product stream wherein the gas to oil ratio and the pressure are configured for the selectivity slope, (% HDS−% OSAT)/(% OSAT*(100−% HDS)), to be above 0.55, and to provide a lower octane loss at all severities above 60% HDS, compared to compared to all prior reported processes with similar conversion of organic sulfur with a lower gas to oil ratio, as measured by the selectivity slope.