Agents for lightening keratin fibers include, relative to their weight, 20 to 75 wt.-% oil(s), 0.05 to 5 wt.-% xanthan, 1 to 70 wt.-% peroxodisulfate(s) and 1 to 15 wt.-% cetearyl alcohol. The agents have increased storage stability, not only the physical stability (settling, phase separation) but also the chemical stability (degradation of the persalts) thereof being improved.