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-ethlyenically unsaturated C3-C8 carboxylic acid and at least one out of glycidyl methacrylate, glycidyl acrylate, allyl methacrylate and allyl acrylate, in the presence of a starch derivative. Optionally, an additional monomer is an ethylenically unsaturated sulfonic acid, an ethylenically unsaturated other monomer or both of them. 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.