A method for reducing the amount of sulfur-containing compounds in a hydrotreated transportation fuel liquid hydrocarbon feedstream, such as diesel or gasoline, having sulfur-containing compounds comprising: a. mixing, in order to oxidize the sulfur-containing compounds to form their corresponding sulfoxides and sulfones, the liquid hydrocarbon feedstream with a catalytic reaction mixture that includes i) 0.5-1 weight % of oxidizing agent, wherein the oxidizing agent is chosen from H 2 O 2 , or aqueous or polar organic acid-soluble organic peroxides, and ii) 1-2 weight % of a catalyst that is a transition metal salt selected from the group consisting of (NH 4 ) 2 WO 4 , (NH 4 ) 6 W 12 O 40· H 2 O, Na 2 WO 4 , Li 2 WO 4 , K 2 WO 4 , MgWO 4 , (NH 4 ) 2 MoO 4 , (NH 4 )6Mo 7 O 24· 4H 2 O, MnO and NaVO 3 , in less than 5% organic acid, wherein the organic acid is one or more carboxylic acids, wherein the peroxide, the at least one carboxylic acid and the transition metal salt form the polar phase system, and to form a biphasic mixture of the liquid hydrocarbon portion and the aqueous mixture of the peroxide, carboxylic acid and catalyst; wherein the reaction is carried out at a temperature in the range of from 50 °C to 90 °C and at a pressure from 1 bar to 100 bars; b. discontinuing the mixing when the amount of sulfur-containing compounds in the mixture have been oxidized to a predetermined level; c. allowing the mixture to separate into an upper hydrocarbon layer and a lower aqueous layer containing the newly-formed sulfoxides and sulfones dissolved in the aqueous mixture portion of the biphasic mixture; d. recovering the hydrocarbon layer; and e. treating the hydrocarbon layer to remove any oxidized sulfur-containing compounds carried over from the separation of step (c). a. mixing, in order to oxidize the sulfur-containing compounds to form their corresponding sulfoxides and sulfones, the liquid hydrocarbon feedstream with a catalytic reaction mixture that includes i) 0.5-1 weight % of oxidizing agent, wherein the oxidizing agent is chosen from H 2 O 2 , or aqueous or polar organic acid-soluble organic peroxides, and ii) 1-2 weight % of a catalyst that is a transition metal salt selected from the group consisting of (NH 4 ) 2 WO 4 , (NH 4 ) 6 W 12 O 40· H 2 O, Na 2 WO 4 , Li 2 WO 4 , K 2 WO 4 , MgWO 4 , (NH 4 ) 2 MoO 4 , (NH 4 )6Mo 7 O 24· 4H 2 O, MnO and NaVO 3 , in less than 5% organic acid, wherein the organic acid is one or more carboxylic acids, wherein the peroxide, the at least one carboxylic acid and the transition metal salt form the polar phase system, and to form a biphasic mixture of the liquid hydrocarbon portion and the aqueous mixture of the peroxide, carboxylic acid and catalyst; wherein the reaction is carried out at a temperature in the range of from 50 °C to 90 °C and at a pressure from 1 bar to 100 bars; b. discontinuing the mixing when the amount of sulfur-containing compounds in the mixture have been oxidized to a predetermined level; c. allowing the mixture to separate into an upper hydrocarbon layer and a lower aqueous layer containing the newly-formed sulfoxides and sulfones dissolved in the aqueous mixture portion of the biphasic mixture; d. recovering the hydrocarbon layer; and e. treating the hydrocarbon layer to remove any oxidized sulfur-containing compounds carried over from the separation of step (c). <EOS>