A product of reduced sulfur content is produced from an olefin-containing hydrocarbon feedstock which includes sulfur-containing impurities. The feedstock is contacted with an olefin-modification catalyst in a reaction zone under conditions which are effective to produce an intermediate product which has a reduced amount of olefinic unsaturation relative to that of the feedstock as measured by bromine number. The intermediate product is then separated into fractions of different volatility, and the lowest boiling fraction is contacted with a hydrodesulfurization catalyst in the presence of hydrogen under conditions which are effective to convert at least a portion of its sulfur-containing impurities to hydrogen sulfide.