Thermoplastic molding compositions, comprising A) from 10 to 98.9% by weight of at least one thermoplastic polyester, B) from 0.01 to 50% by weight of B1) at least one highly branched or hyperbranched polycarbonate or B2) at least one highly branched or hyperbranched polyester of AxBy type, where x is at least 1.1 and y is at least 2.1 or a mixture of these C) from 0.1 to 10% by weight of at least one epoxidized naturally occurring oil or fatty acid ester, or a mixture of these, and D) from 0 to 60% by weight of other additives, where the total of the percentages by weight of components A) to D) is 100%.