The invention relates to a process for the regeneration of a copper-, zinc- and zirconium oxide-comprising adsorption composition after use thereof for the adsorptive removal of carbon monoxide from substance streams comprising carbon monoxide and at least one olefin, in which the adsorption composition is heated to a temperature in the range from 160 to 400° C. and a regeneration gas is passed through the adsorption composition, wherein the regeneration gas comprises 1000 to 3000 ppm of oxygen in an inert carrier gas.