The invention relates to a process for preparing an aqueous dispersion of a polymer P, which comprises the emulsion polymerization of vinyl acetate, an acrylate monomer, which is a C1-C10 alkyl acrylate or a C1-C10 methacrylate, an α,β-ethylenically unsaturated C3-C8 carboxylic acid, glycidyl methacrylate or glycidyl acrylate, optionally an ethylenically unsaturated sulfonic acid and optionally an ethylenically unsaturated other monomer. Furthermore, the aqueous polymer dispersion obtainable from this process and a powder form thereof are disclosed. They are useful for a paper coating slip containing one of the aforementioned forms. A paper or a cardboard, which is coated with the paper coating slip, shows surface strength, which is expressed by a good dry pick resistance, a good wet pick resistance or good offset test results. The aqueous polymer dispersion or the powder form thereof is furthermore useful as a binder.