A process produces a polymer composition (A) containing a styrene copolymer (a) and an impact modifier (b), comprising a copolymer (b1) as graft base and a graft (b2), where the steps of the process are: (1) providing a crosslinked copolymer (b1) made of: (b11) from 70 to 99.99% by weight of a conjugated diene or acrylate, (b12) from 0 to 29% by weight of another comonomer, (b13) from 0 to 10% by weight of crosslinking monomers, and (b14) from 0.01 to 0.7% by weight of a chain-transfer reagent; (2) applying, to the copolymer (b1), at least one graft (b2) comprising: (b21) from 65 to 95% by weight of a vinylaromatic monomer, (b22) from 5 to 35% by weight of acrylonitrile and/or methacrylonitrile, and (b23) from 0 to 30% by weight of monoethylenically unsaturated monomers, thus providing the impact modifier (b); (3) mixing the styrene copolymer (a) and the impact modifier (b), and thus leads to improved mechanical properties of the polymer composition (A).