Thermoplastic molding compositions comprising A) from 40 to 96% by weight of a semiaromatic polyamide, B) from 2 to 30% by weight of a copolymer composed of B1) from 35 to 89.9% by weight of ethylene, B2) from 10 to 60% by weight of 1-octene or 1-butene or propylene or a mixture of these, and B3) from 0.05 to 5% by weight of functional monomers, where the functional monomers have been selected from the group of the carboxylic acid groups, carboxylic anhydride groups, carboxylic ester groups, carboxamide groups, carboximide groups, amino groups, hydroxy groups, epoxy groups, urethane groups, or oxazoline groups, or a mixture of these, C) from 1 to 50% by weight of fibrous or particulate fillers, or a mixture of these, D) from 0.1 to 10% by weight of D1) 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 D2) 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, E) from 0 to 15% by weight of an electrically conductive additive, F) from 0 to 30% by weight of further additives, where the total of the percentages by weight of components A) to F) is 100%.