A process for preparing an aqueous polymer dispersion through free-radical-initiated emulsion polymerization, wherein at least one ethylenically unsaturated compound (monomer P) undergoes free-radical polymerization in the presence of a copolymer A in an aqueous medium, wherein a) the copolymer A is formed in copolymerized form from ≥ 10% and ≤ 50% by weight of at least one α,β-monoethylenically unsaturated C 3 to C 6 monocarboxylic acid (monomers A1), ≥ 50% and ≤ 90% by weight of at least one other monoethylenically unsaturated compound (monomers A2), wherein the amounts of monomers A1 and A2 add up to 100% by weight (total amount of monomers A), and wherein • the copolymer A has a weight-average molecular weight in the range ≥ 5000 and ≤ 20 000 g/mol, wherein the weight-average molecular weight is determined by gelpermeation chromatography using defined polystyrene standards dissolved in tetrahydrofuran for calibration, • the type and amounts of monomers A1 and A2 are chosen such that the copolymer A obtained has a glass transition temperature Tg measured according to DIN EN ISO 11357-2 in the range ≥ 70°C, and wherein • before the addition and the free-radical polymerization of the at least one monomer P, the copolymer A is reacted in an aqueous medium with a metal compound M, selected from the group comprising oxides, hydroxides, carbonates or hydrogen carbonates of magnesium, calcium or zinc, and a base B that differs from the metal compound M, such that • ≥ 50 mol% of the carboxyl groups present in the copolymer A have been neutralized by the base B, and • the amount of the metal compound M is 0.01% to 5% by weight based on the amount of copolymer A, b) the type and amount of the at least one monomer P are chosen such that the dispersion polymer P obtained has a glass transition temperature Tg measured in accordance with DIN EN ISO 11357-2 in the range ≥ -30°C and ≤ 90°C, and wherein c) the ratio of the amounts by weight of copolymer A to the at least one monomer P used to prepare the dispersion polymer P is in the range ≥ 15 and ≤ 60 to ≥ 40 and ≤ 85. a) the copolymer A is formed in copolymerized form from ≥ 10% and ≤ 50% by weight of at least one α,β-monoethylenically unsaturated C 3 to C 6 monocarboxylic acid (monomers A1), ≥ 50% and ≤ 90% by weight of at least one other monoethylenically unsaturated compound (monomers A2), wherein the amounts of monomers A1 and A2 add up to 100% by weight (total amount of monomers A), and wherein • the copolymer A has a weight-average molecular weight in the range ≥ 5000 and ≤ 20 000 g/mol, wherein the weight-average molecular weight is determined by gelpermeation chromatography using defined polystyrene standards dissolved in tetrahydrofuran for calibration, • the type and amounts of monomers A1 and A2 are chosen such that the copolymer A obtained has a glass transition temperature Tg measured according to DIN EN ISO 11357-2 in the range ≥ 70°C, and wherein • before the addition and the free-radical polymerization of the at least one monomer P, the copolymer A is reacted in an aqueous medium with a metal compound M, selected from the group comprising oxides, hydroxides, carbonates or hydrogen carbonates of magnesium, calcium or zinc, and a base B that differs from the metal compound M, such that • ≥ 50 mol% of the carboxyl groups present in the copolymer A have been neutralized by the base B, and • the amount of the metal compound M is 0.01% to 5% by weight based on the amount of copolymer A, ≥ 50% and ≤ 90% by weight of at least one other monoethylenically unsaturated compound (monomers A2), wherein the amounts of monomers A1 and A2 add up to 100% by weight (total amount of monomers A), and wherein • the copolymer A has a weight-average molecular weight in the range ≥ 5000 and ≤ 20 000 g/mol, wherein the weight-average molecular weight is determined by gelpermeation chromatography using defined polystyrene standards dissolved in tetrahydrofuran for calibration, • the type and amounts of monomers A1 and A2 are chosen such that the copolymer A obtained has a glass transition temperature Tg measured according to DIN EN ISO 11357-2 in the range ≥ 70°C, and wherein • before the addition and the free-radical polymerization of the at least one monomer P, the copolymer A is reacted in an aqueous medium with a metal compound M, selected from the group comprising oxides, hydroxides, carbonates or hydrogen carbonates of magnesium, calcium or zinc, and a base B that differs from the metal compound M, such that • ≥ 50 mol% of the carboxyl groups present in the copolymer A have been neutralized by the base B, and • the amount of the metal compound M is 0.01% to 5% by weight based on the amount of copolymer A, b) the type and amount of the at least one monomer P are chosen such that the dispersion polymer P obtained has a glass transition temperature Tg measured in accordance with DIN EN ISO 11357-2 in the range ≥ -30°C and ≤ 90°C, and wherein c) the ratio of the amounts by weight of copolymer A to the at least one monomer P used to prepare the dispersion polymer P is in the range ≥ 15 and ≤ 60 to ≥ 40 and ≤ 85.