Binder systems for high-gloss coatings and processes for producing them are provided, where the binder systems are prepared by preparing an aqueous polymer dispersion by radically initiated aqueous emulsion polymerization using defined first and second polymerization stages wherein the weight ratio of the sum of the total amounts of first polymerization stage monomers A1 to C1 (total monomer amount 1) to the sum of the total amounts of second polymerization stage monomers A2 to C2 (total monomer amount 2) is in the range 5:95 to 70:30, the amount of chain transfer agent in the second polymerization stage is selected such that the resulting overall polymer has a weight-average molecular weight of ≥15 000 and ≤50 000 g/mol, and the amount of the dispersing assistant is ≤3.0 wt %, based on the sum of total monomer amount 1 and total monomer amount 2 (total monomer amount).