A description is given of an aqueous polymer dispersion comprising a polymer which is obtainable by emulsion polymerization from a monomer mixture comprising as hydrophilic monomers ethoxylated (meth)acrylate monomer, acid monomer, and C1 to C20 hydroxyalkyl(meth)acrylate; and also at least one hydrophobic principal monomer, selected from C1 to C20 alkyl(meth)acrylates and vinylaromatics; and also, optionally, further monomers. This polymer is preparable by at least two-stage emulsion polymerization, where in a first polymerization stage the predominant fraction or the entire amount of the hydrophilic monomers is used, and in a later polymerization stage the predominant fraction or the entire amount of the hydrophobic monomers is used. The polymer dispersion is a suitable binder for aqueous particle dispersions, more particularly of sound deadener compositions, which comprise inorganic and optionally also organic particulate solids. Also described is a method for damping oscillations or vibrations of vehicle components.