The invention relates to a polymer synthesized from 0.5 to 30% by weight of vinyl acetate (a), from 0.1 to 10% by weight of monomer containing at least one acid or acid anhydride group (b), from 5 to 70% by weight of at least one monomer other than (a) and (b), having a solubility of more than 5 g/l water (21.degree. C., 1 bar) and a glass transition temperature of less than 15.degree. C. (c), from 0 to 20% by weight of a vinylaromatic monomer having a solubility of less than 5 g/l water (d), from 0 to 90% by weight of at least one C.sub.1 to C.sub.20 alkyl (meth)acrylate (e) other than (a) to (d), and from 0 to 40% by weight of at least one further monomer (f) other than (a) to (e).