A flame-retardant mixture comprising components (i) and (ii); or (i), (ii) and (iii): i) at least one brominated vinylaromatic-diene block copolymer (Br-SBC-1) comprising at least one vinylaromatic polymer block S and at least one brominated diene polymer block BB, in which the weight-average molar mass M w of the block S before bromination is not less than M w of the block BB; ii) at least one further brominated vinylaromatic-diene block copolymer (Br-SBC-2) comprising at least one vinylaromatic polymer block H, at least one brominated diene polymer block BD and no vinylaromatic polymer block S, in which the weight-average molar mass M w of the block H before bromination is less than M w of the block BD, and the proportion of the diene polymer, especially of the polybutadiene, is more than 60% by weight, based on the Br-SBC-2 block copolymer; iii) at least one brominated diene homopolymer and/or brominated random diene copolymer, having a weight-average molar mass M w before bromination of not more than M w of the block BB of component (i); wherein • the molar mass M w of the block BB in the Br-SBC-1 block copolymer (before bromination) is from 50 000 to 130 000 g/mol and the molar mass M w of the block S is from 60 000 to 300 000 g/mol; and • the components (i) and (ii); or (i), (ii) and (iii) are present as follows: (i) 0.5 to 50% by weight and (ii) 50 to 99.5% by weight; or (i) 0.50 to 50% by weight, (ii) 50 to 99.49% by weight and (iii) 0.01 to 49% by weight; where the sum total of components (i) and (ii); or (i), (ii) and (iii); in each case is 100% by weight; and determination of molar mass M w is carried out before bromination by GPC according to ISO 16014-3:2012 (relative to polystyrene standards at 25°C in THF). i) at least one brominated vinylaromatic-diene block copolymer (Br-SBC-1) comprising at least one vinylaromatic polymer block S and at least one brominated diene polymer block BB, in which the weight-average molar mass M w of the block S before bromination is not less than M w of the block BB; ii) at least one further brominated vinylaromatic-diene block copolymer (Br-SBC-2) comprising at least one vinylaromatic polymer block H, at least one brominated diene polymer block BD and no vinylaromatic polymer block S, in which the weight-average molar mass M w of the block H before bromination is less than M w of the block BD, and the proportion of the diene polymer, especially of the polybutadiene, is more than 60% by weight, based on the Br-SBC-2 block copolymer; iii) at least one brominated diene homopolymer and/or brominated random diene copolymer, • the molar mass M w of the block BB in the Br-SBC-1 block copolymer (before bromination) is from 50 000 to 130 000 g/mol and the molar mass M w of the block S is from 60 000 to 300 000 g/mol; and • the components (i) and (ii); or (i), (ii) and (iii) are present as follows: (i) 0.5 to 50% by weight and (ii) 50 to 99.5% by weight; or (i) 0.50 to 50% by weight, (ii) 50 to 99.49% by weight and (iii) 0.01 to 49% by weight; (i) 0.5 to 50% by weight and (ii) 50 to 99.5% by weight; or (i) 0.50 to 50% by weight, (ii) 50 to 99.49% by weight and (iii) 0.01 to 49% by weight; (i) 0.50 to 50% by weight, (ii) 50 to 99.49% by weight and (iii) 0.01 to 49% by weight;