An agent for dyeing and/or bleaching keratin fibers, in particular human hair, including in a cosmetic carrier (a) at least one fatty alcohol selected from the group of arachyl alcohol (eicosan-1-ol), gadoleyl alcohol ((9Z)-eicos-9-en-1-ol), arachidonic alcohol ((5Z,8Z,11Z,14Z)-eicosa-5,8,11,14-tetraen-1-ol), heneicosyl alcohol (heneicosan-1-ol), behenyl alcohol (docosan-1-ol), erucyl alcohol ((13Z)-docos-13-en-1-ol) and brassidyl alcohol ((13E)-docosen-1-ol), (b) at least one persulfate salt selected from the group of ammonium persulfate, potassium persulfate and sodium persulfate, and (c) at least one glyceryl fatty acid ester of general formula (I), in which R1, R2 and R3 independently of one another stand for a hydrogen atom or a grouping of formula (II), in which R4 stands for an unbranched or branched, saturated or unsaturated C11-C28 alkyl group, with the proviso that at least one and at most two of the radicals selected from R1, R2 and R3 stand for a grouping of formula (II).
