Thermoplastic molding compositions, comprising A) from 10 to 98% by weight of at least one thermoplastic polymer, B) from 0.01 to 50% by weight of B1) at least one highly branched or hyperbranched polycarbonate with an OH number of from 1 to 600 mg KOH/g of polycarbonate (to DIN 53240, part 2), 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 1 to 30% by weight of a flame retardant combination composed of, based on 100% by weight of C), C1) from 20 to 99% by weight of a halogen-containing flame retardant, C2) from 1 to 80% by weight of an antimony oxide, 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%.