Cosmetic agent for lightening keratin fibers, containing at least one packaged preparation (A), wherein the preparation (A), based on its total weight, containsa) from about 10 to about 90% by weight of peroxydisulfate(s)b) from about 10 to about 50% by weight of sodium silicateand the preparation (A) is packaged in a water-soluble film which, based on its total weight, includes at least 60% by weight of a polymer mixture which has a multi-modal molecular weight distribution, exemplified in that the sodium silicate comprises sodium disilicate and methods for the use of this agent.