Process of extracting sulphur-containing compounds from a hydrocarbon cut of the gasoline or LPG type by liquid-liquid extraction with a soda solution employing a unit (2) for pretreatment of the feedstock to be treated located upstream of the unit (4) for extraction with soda, said pretreatment unit consisting of a first pretreatment reactor operating in batch mode followed by a second continuous reactor of the piston type operating in piston mode.