The invention provides water-soluble or water-swellable copolymers obtained by free-radical copolymerization ofA) acryloyldimethyltaurine and/or acryloyldimethyltaurates,B) optionally, one or more 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,C) one or more at least monofunctional, silicon-containing components capable of free-radical polymerization, the copolymerizationD) taking place in the presence of at least one polymeric additive having number-average molecular weights of from 200 g/mol to 109 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.