Compositions comprising A) 70 to 95 parts by weight of at least one polymer selected from the group consisting of aromatic polycarbonate and aromatic polyester carbonate, B) 1 to 10 parts by weight of a mixture comprising at least one polybutadiene-based graft polymer and at least one butadiene-free vinyl (co)polymer, C) 1 to 20 parts by weight of at least one phosphorus-containing flame retardant selected from the group consisting of phosphonate amines, phosphazenes and monomeric and oligomeric phosphoric and phosphonic esters of the general formula in which R 1, R 2, R 3 and R 4 are each independently optionally halogenated C 1 to C 8 -alkyl, in each case optionally alkyl-substituted, preferably C 1 to C 4 -alkyl-substituted, and/or halogen-substituted, preferably chlorine- or bromine-substituted, C 5 to C 6 -cycloalkyl, C 6 to C 20 -aryl or C 7 to C 12 -aralkyl, n is independently 0 or 1 q is 0 to 30 X is a polycyclic aromatic radical having 12 to 30 carbon atoms, or a linear or branched aliphatic radical having 2 to 30 carbon atoms, which may be OH-substituted and may contain up to 8 ether bonds, D) 0.1 to 20.0 parts by weight (based in each case on the sum total of components A to C) of at least one polymer additive, where the polybutadiene content based on the sum total of the parts by weight of components A to C is 0.5% to 5.5% by weight, and where the total content of butadiene-free vinyl (co)polymer from component B based on the sum total of components A to C is 0.5% to 5.0% by weight, and where the compositions are free of thermoplastic polyesters such as polyalkylene terephthalates, and where the sum total of the parts by weight of components A, B and C in the polycarbonate composition is normalized to 100. A) 70 to 95 parts by weight of at least one polymer selected from the group consisting of aromatic polycarbonate and aromatic polyester carbonate, B) 1 to 10 parts by weight of a mixture comprising at least one polybutadiene-based graft polymer and at least one butadiene-free vinyl (co)polymer, C) 1 to 20 parts by weight of at least one phosphorus-containing flame retardant selected from the group consisting of phosphonate amines, phosphazenes and monomeric and oligomeric phosphoric and phosphonic esters of the general formula in which R 1, R 2, R 3 and R 4 are each independently optionally halogenated C 1 to C 8 -alkyl, in each case optionally alkyl-substituted, preferably C 1 to C 4 -alkyl-substituted, and/or halogen-substituted, preferably chlorine- or bromine-substituted, C 5 to C 6 -cycloalkyl, C 6 to C 20 -aryl or C 7 to C 12 -aralkyl, n is independently 0 or 1 q is 0 to 30 X is a polycyclic aromatic radical having 12 to 30 carbon atoms, or a linear or branched aliphatic radical having 2 to 30 carbon atoms, which may be OH-substituted and may contain up to 8 ether bonds, R 1, R 2, R 3 and R 4 are each independently optionally halogenated C 1 to C 8 -alkyl, in each case optionally alkyl-substituted, preferably C 1 to C 4 -alkyl-substituted, and/or halogen-substituted, preferably chlorine- or bromine-substituted, C 5 to C 6 -cycloalkyl, C 6 to C 20 -aryl or C 7 to C 12 -aralkyl, n is independently 0 or 1 q is 0 to 30 X is a polycyclic aromatic radical having 12 to 30 carbon atoms, or a linear or branched aliphatic radical having 2 to 30 carbon atoms, which may be OH-substituted and may contain up to 8 ether bonds, D) 0.1 to 20.0 parts by weight (based in each case on the sum total of components A to C) of at least one polymer additive,