The invention relates to a process for increasing the bleaching efficiency of an inorganic persalt and to bleaching and/or detergent compositions suitable for removing stains from textiles or from other products such as paper, cellulose, cork, hair etc. These bleaching and/or detergent and/or anti-incrusting compositions comprise an inorganic persalt and an activating agent comprising an acetylated mixture of sorbitol and mannitol wherein the molar ratio between the bleaching activator and the persalt is usually from 10:90 to 50:50. The bleaching activator having an acetylation degree ranging from 1 to 6 and the weight ratio of sorbitol to mannitol in the mixture is within the range of from 2.5:1 to 4:1.