Agents for lightening keratinic fibers, which include, based on their weight, 20 to 75% by weight of oil(s), 0.05 to 5% by weight of polymer(s) from the group of ethylene/propylene/styrene copolymers and/or butylene/ethylene/styrene copolymers and/or butylene/propylene/styrene copolymers, and 1 to 70% by weight of peroxydisulfate(s), whereby the weight ratio of sodium peroxydisulfate in the agent to the total amount of peroxydisulfates in the agent is at least 0.2, possess increased storage stability, the improvement being not only in physical stability (sedimentation, phase separation) but also in chemical stability (degradation of the persalts). There are also improvements in product yield, spreadability of the application mixture, and the bleaching effect.