Polymer-containing transparent bleaching with proteins and / or silicones

The present invention, in a first embodiment of means for lightening keratin fibers, comprising at least two separately packed preparations (A) and (B) and optionally a further packaged separately from (A) and (B) preparation (C), which immediately are mixed prior to application to an application mixture, wherein said composition contains (a) at least one persulfate, at least an acrylate polymer, and carboxymethyl cellulose, and the preparation (B) is free-flowing and contains at least one oxidizing agent, and preparation (a) - based on its weight - a1) 0 to 3 wt .-% keratin hydrolyzate (s) and / or a2) 0 to 5 wt .-% silicone oil (e) includes, with the proviso that the preparation (A) - based on its weight - 0.1 to 6 wt .-% of compound (s) from the groups a1) and a2) contains.