The present invention provides very finely divided polymer dispersions obtainable by at least one two-stage emulsion polymerization, wherein 1) an acid-rich first polymer P1 is prepared by a radical polymerization from a 1st composition comprising A) at least one monomer selected from the group of (cyclo)alkyl (meth)acrylates, vinylaromatics having up to 20 carbon atoms, a radically polymerizable compound selected from the group of ethylenically unsaturated nitriles having up to 20 carbon atoms, vinyl esters of carboxylic acids containing up to 20 carbon atoms, vinyl halides having up to 10 carbon atoms, and vinyl ethers of alcohols containing 1 to 10 carbon atoms B) at least one α,β-ethylenically unsaturated carboxylic acid C) at least one crosslinking monomer with a keto or aldehyde group D) optionally at least one adhesion promoter E) optionally tert-butyl acrylate F) optionally further monomers M in the presence of a chain link transfer agent, 2) the polymer P1 prepared under 1) is admixed with a base, 3) a hydrophobic polymer P2 is prepared by radical polymerization, in the presence of the polymer P1 treated under 2), from a 2nd composition comprising A) at least one monomer selected from the group of (cyclo)alkyl (meth)acrylates, vinylaromatics having up to 20 carbon atoms, a radically polymerizable compound selected from the group of ethylenically unsaturated nitriles having up to 20 carbon atoms, vinyl esters of carboxylic acids containing up to 20 carbon atoms, vinyl halides having up to 10 carbon atoms, and vinyl ethers of alcohols containing 1 to 10 carbon atoms B) optionally at least one α,β-ethylenically unsaturated carboxylic acid C) at least one crosslinking monomer with a keto or aldehyde group D) optionally at least one adhesion promoter, and also E) optionally further monomers M, 4) and by optional addition, subsequent to the polymerization of P1 and P2, of a water-soluble at least trifunctional alkoxylated polyamine, more particularly an ethoxylated and/or propoxylated triamine.