A water-soluble or water-swellable copolymer obtainable by free-radical copolymerization of A) acryloyldimethyltaurine and/or acryloyldimethyltaurates, the degree of neutralization being more than 80%, B) if desired, one or more other olefinically unsaturated, noncationic, 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 olefinically unsaturated, cationic comonomers containing at least one oxygen, nitrogen, sulfur or phosphorus atom and possessing a molecular weight of less than 500 g/mol, and which comprise [2-(methacryloyloxy)ethyl]trimethylammonium chloride,[2-(acryloyloxy)ethyl]trimethylammonium chloride, [2-methacrylamidoethyl]trimethylammonium chloride, [2-(acrylamido)ethyl]trimethylammonium chloride, N-methyl-2-vinylpyridinium chloride and/or N-methyl-4-vinylpyridinium chloride, D) if desired, one or more at least monofunctional, silicon-containing components capable of free-radical polymerization, E) if desired, one or more at least monofunctional, fluorine-containing components capable of free-radical polymerization, F) if desired, one or more mono- or polyolefinically unsaturated, optionally crosslinking macromonomers each possessing at least one oxygen, nitrogen, sulfur or phosphorus atom and having a number-average molecular weight of greater than or equal to 200 g/mol, the macromonomers not being a silicon-containing component D) or fluorine-containing component E), G) the copolymerization taking place in the presence of at least one polymeric additive having number-average molecular weights of from 200 g/mol to 10 9 g/mol, which comprises homopolymers and copolymers of N-vinylformamide, N-vinylacetamide, N-vinylpyrrolidone, ethylene oxide, propylene oxide, acryloyldimethyltaurine, N-vinylcaprolactone, N-viriylmethylacetamide, acrylamide, acrylic acid, methacrylic acid, N-vinylmorpholide, hydroxymethyl methacrylate, diallyldimethylammonium chloride (DADMAC) and/or [2-(methacryloyloxy)ethyl]trimethylammonium chloride; polyalkylene glycols and/or alkylpolyglycols, H) with the proviso that component A) is copolymerized with at least two components selected from at least two of the groups C) to F), wherein the amount of acryloyldimethyltaurine and/or acryloyldimethyltaurates, based on the total mass of the copolymers, is from 50 to 99.5% by weight. A) acryloyldimethyltaurine and/or acryloyldimethyltaurates, the degree of neutralization being more than 80%, B) if desired, one or more other olefinically unsaturated, noncationic, 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 olefinically unsaturated, cationic comonomers containing at least one oxygen, nitrogen, sulfur or phosphorus atom and possessing a molecular weight of less than 500 g/mol, and which comprise [2-(methacryloyloxy)ethyl]trimethylammonium chloride,[2-(acryloyloxy)ethyl]trimethylammonium chloride, [2-methacrylamidoethyl]trimethylammonium chloride, [2-(acrylamido)ethyl]trimethylammonium chloride, N-methyl-2-vinylpyridinium chloride and/or N-methyl-4-vinylpyridinium chloride, D) if desired, one or more at least monofunctional, silicon-containing components capable of free-radical polymerization, E) if desired, one or more at least monofunctional, fluorine-containing components capable of free-radical polymerization, F) if desired, one or more mono- or polyolefinically unsaturated, optionally crosslinking macromonomers each possessing at least one oxygen, nitrogen, sulfur or phosphorus atom and having a number-average molecular weight of greater than or equal to 200 g/mol, the macromonomers not being a silicon-containing component D) or fluorine-containing component E), G) the copolymerization taking place in the presence of at least one polymeric additive having number-average molecular weights of from 200 g/mol to 10 9 g/mol, which comprises homopolymers and copolymers of N-vinylformamide, N-vinylacetamide, N-vinylpyrrolidone, ethylene oxide, propylene oxide, acryloyldimethyltaurine, N-vinylcaprolactone, N-viriylmethylacetamide, acrylamide, acrylic acid, methacrylic acid, N-vinylmorpholide, hydroxymethyl methacrylate, diallyldimethylammonium chloride (DADMAC) and/or [2-(methacryloyloxy)ethyl]trimethylammonium chloride; polyalkylene glycols and/or alkylpolyglycols, H) with the proviso that component A) is copolymerized with at least two components selected from at least two of the groups C) to F),