Thermoplastic molding compositions, comprisingE) from 10 to 99.9% by weight of a thermoplastic polymer,F) from 0.01 to 10% by weight of a copolymer obtainable via free-radical-initiated aqueous emulsion polymerization of ethylenically unsaturated monomers in the presence of at least one dispersing agent and of at least one free-radical initiator by the feed process, where the emulsion polymerization uses from 70 to 99.5% by weight of α,β-monoethylenically unsaturated compounds [monomers A], and from 0.5 to 30% by weight of compounds having at least two ethylenically unsaturated groups capable of free-radical copolymerization [monomers B], and also, if appropriate, up to 5% by weight of α,β-monoethylenically unsaturated mono- or dicarboxylic acids having from 3 to 6 carbon atoms and/or their amides [monomers C], where the monomers A to C give a total of 100% by weight (entire amount of monomers) and the monomer feeds take place in such a way that ≧60% by weight of the entire amount of monomers B are fed to the polymerization mixture under polymerization conditions at a juncture after ≧60% by weight of the entire amount of monomer have been fed to the polymerization mixture under polymerization conditions, from 0 to 70% by weight of further additives,where the total of the percentages by weight of components A) to C) gives 100%.