A one-step process for desulfurizing an oxidized sulfone-containing fuel stream, such as a diesel stream, is disclosed where mass transfer and conversion of sulfone occurs simultaneously such that the sulfur atom in sulfone molecule is removed as sulfite to provide a low-sulfur diesel stream. The diesel stream for treatment is obtained as a result of the oxidation of a thiophene-rich diesel stream with an oxidant to provide a sulfone-containing diesel stream. The one-step process uses a single vessel having a shroud of vertical hanging fibers to affect the mass transfer of sulfones in diesel into contacting with an aqueous solution of alkali metal hydroxide where it is converted to sulfite and biphenyls. The sulfite-rich aqueous solution and low sulfur diesel are then separately removed from the vessel.