Polymer compositions comprising A) 45 to 95 parts by weight, based on the sum total of A and B, where the parts by weight of A and B add up to 100, of aromatic polycarbonate and/or polyestercarbonate having weight-average molecular weight M w measured by GPC in methylene chloride at 25°C using polycarbonate standards of 26 000 to 31 000 g/mol, B) 5 to 55 parts by weight, based on the sum total of A and B, of a mixture comprising B1) at least one graft polymer prepared in an emulsion polymerization process, B2) at least one graft polymer prepared in a bulk, suspension or solution polymerization process and having a median particle size of 0.3 to 0.6 μm determined by ultracentrifugation. B3) optionally a rubber-free vinyl (co)polymer and C) 0 to 30 parts by weight, based on the sum total on A and B, of at least one commercial polymer additive, characterized in that (i) the composition contains a total of less than 2.0% by weight of graft particles composed of components B1 and B2 having a corresponding graft particle diameter exceeding 800 nm determined by ultracentrifugation, and contains a total of less than 2.0% by weight of graft particles composed of components B1 and B2 having a corresponding graft particle diameter below 100 nm determined by ultracentrifugation, and (ii) the graft polymer of component B1 is prepared by grafting a mixture (B1.1) of vinylic compounds onto a particulate elastomeric graft base (B1.2), this grafting reaction being initiated using an inorganic persulfate compound as polymerization initiator, and (iii) the composition is free of graft polymers prepared in the emulsion polymerization process which have been prepared using redox-based polymerization initiator systems, and (iv) in which the total butadiene content from the graft bases B1.2 and B2.2, based on the overall composition, is 5 to 12% by weight. A) 45 to 95 parts by weight, based on the sum total of A and B, where the parts by weight of A and B add up to 100, of aromatic polycarbonate and/or polyestercarbonate having weight-average molecular weight M w measured by GPC in methylene chloride at 25°C using polycarbonate standards of 26 000 to 31 000 g/mol, B) 5 to 55 parts by weight, based on the sum total of A and B, of a mixture comprising B1) at least one graft polymer prepared in an emulsion polymerization process, B2) at least one graft polymer prepared in a bulk, suspension or solution polymerization process and having a median particle size of 0.3 to 0.6 μm determined by ultracentrifugation. B3) optionally a rubber-free vinyl (co)polymer and B1) at least one graft polymer prepared in an emulsion polymerization process, B2) at least one graft polymer prepared in a bulk, suspension or solution polymerization process and having a median particle size of 0.3 to 0.6 μm determined by ultracentrifugation. B3) optionally a rubber-free vinyl (co)polymer and C) 0 to 30 parts by weight, based on the sum total on A and B, of at least one commercial polymer additive, (i) the composition contains a total of less than 2.0% by weight of graft particles composed of components B1 and B2 having a corresponding graft particle diameter exceeding 800 nm determined by ultracentrifugation, and contains a total of less than 2.0% by weight of graft particles composed of components B1 and B2 having a corresponding graft particle diameter below 100 nm determined by ultracentrifugation, and (ii) the graft polymer of component B1 is prepared by grafting a mixture (B1.1) of vinylic compounds onto a particulate elastomeric graft base (B1.2), this grafting reaction being initiated using an inorganic persulfate compound as polymerization initiator, and (iii) the composition is free of graft polymers prepared in the emulsion polymerization process which have been prepared using redox-based polymerization initiator systems, and (iv) in which the total butadiene content from the graft bases B1.2 and B2.2, based on the overall composition, is 5 to 12% by weight.