A process for preparing an aqueous styrene-butadiene polymer dispersion by free-radical aqueous emulsion polymerization of a monomer mixture M containing from 40 to 80% by weight of styrene as monomer M1, from 20 to 60% by weight of butadiene as monomer M2, and from 0 to 40% by weight, based on 100% by weight of monomers, of ethylenically unsaturated comonomers M3 other than styrene and butadiene by a monomer feed technique in the presence of from 0.05 to 0.5% by weight, based on 100% by weight of monomers, of at least one hydrocarbon HC having 6 to 20 carbon atoms selected from compounds which on abstraction of a hydrogen atom form a pentadienyl radical or a 1-phenylallyl radical and α-methylstyrene dimer comprises raising, at a point in time when at least 70% of the monomers to be polymerized have been supplied to the polymerization reaction, the concentration of butadiene in the monomer feed for a period of at least 1% of the total feed time by at least 10% by weight, based on monomers in the feed.