A process for preparing an aqueous styrene-butadiene polymer dispersion by free-radical aqueous emulsion polymerization of a monomer mixture M that comprises styrene, butadiene, and if desired up to 30% by weight, per 100% by weight of monomers, of ethylenically unsaturated comonomers other than styrene and butadiene; by a monomer feed technique that includes supplying to the polymerization reaction a regulator system containing, from 0.02 to 0.4% by weight of terpinolene and from 0.5 to 2% by weight of an organic compound S containing at least one SH group.