The invention provides water-soluble or water-swellable copolymers obtained by free-radical copolymerization of A) acryloyldimethyltaurine and/or acryloyldimethyltaurates, B) if desired, one or more other olefinically unsaturated, optionally crosslinking comonomers containing at least one oxygen, nitrogen, sulfur or phosphorus atom and possessing a molecular weight of less than 500 g/mol, the copolymerization C) taking place in the presence of at least one polymeric additive having a number-average molecular weight of from 200 g/mol to 10.sup.9 g/mol. The water-soluble or water-swellable copolymers of the present invention are useful in paper processing, laundry detergents, textile processing, petroleum extraction and formulating cosmetics.