The present invention relates to copolymers, which comprises, in copolymerized form, between 25 and 80% by weight of tert-butyl(meth)acrylate, 2 to 60% by weight of hydroxyalkyl(meth)acrylate, 10 to 40% by weight of an anionic or anionogenic, free-radically polymerizable, olefinically unsaturated compound which is or comprises methacrylic acid, and, if appropriate, up to 30% by weight of a further free-radically polymerizable, olefinically unsaturated compound. In addition, the present invention relates to the use of such copolymers in cosmetic preparations, and to such cosmetic preparations per se.