A process for reducing the odor emission of aqueous vinylaromatic/1,3-diene copolymer dispersions and of redispersion powders obtainable therefrom by drying, is by emulsion polymerization of a mixture containing at least one vinylaromatic and at least one 1,3-diene in the presence of one or more surfactant substances and optionally drying of the polymer dispersion obtained thereby. There are 0.01% to 15.0% by weight of one or more monomers of the branched or straight-chain alkyl esters having 1 to 8 C atoms in the alkyl radical of monounsaturated monocarboxylic or dicarboxylic acids and 0.01% to 15.0% by weight of one or more monomers based upon the vinyl esters of branched or straight-chain aliphatic carboxylic acids having 1 to 10 C atoms which are added in one step or in two successive steps toward the end of the polymerization, when the total content of free monomers in the aqueous copolymer dispersion is in the range from .gtoreq.0 to .ltoreq.20% by weight. It is also possible optionally to add the vinyl ester fraction as early as the beginning of or during the polymerization. The data in % by weight is based in each case on the polymer content of the dispersion.