The invention relates to a process for removing dienes from a material stream comprising C3 to C5 hydrocarbons by selective hydrogenation at a specified reaction pressure and a specified reaction temperature in the presence of a hydrogenation catalyst, wherein the reaction pressure and the reaction temperature at the reactor inlet are regulated such that the reaction pressure at the reactor inlet does not deviate by more than 0.01 bar from the specified reaction pressure and the reaction temperature at the reactor inlet does not deviate by more than 0.1° C. from the specified reaction temperature and the proportion of hydrogen supplied to the selective hydrogenation is in the range from 2 to 20 moles per mole of diene present in the material stream comprising C3 to C5 hydrocarbons.