The present invention relates to a process for preparing polymer powders from aqueous polymer dispersions in which the dispersed polymer P comprises in copolymerized form: i) at least one vinylaromatic monomer (a), ii) 1,3-butadiene as monomer (b), and iii) one or more monomers (c) different than the monomers (a) and (b), which comprises drying the aqueous polymer dispersion in the presence of polyvinyl alcohol as drying agent. The present invention also relates to the polymer powders obtainable by this process and to the use of these polymer powders as binders in paints, varnishes and coating compositions generally, in adhesives, and for modifying mineral construction materials. The present invention also relates to mineral construction materials in the form of dry formulations comprising the polymer powders of the invention.