Polymer mixtures comprise P1) from 1 to 85% by weight of an elastomeric block copolymer which has been built up from hard blocks S made from vinylaromatic monomers and from random soft blocks B/S made up from dienes and from vinylaromatic monomers, and which contains at least the block structure S-B/S-S, where the diene content is less than 50 percent by weight and the proportion of the soft phase formed from the blocks B/S is at least 60 percent by weight, based in each case on the entire block copolymer, P2) from 5 to 89% by weight of a block copolymer differing from P1) and made from vinylaromatic monomers and from dienes, P3) from 10 to 94% by weight of glass-clear or impact-modified polystyrene or mixtures thereof, and P4) from 0 to 84% by weight of other additives, where the total of components P1) to P4) is 100%.