The present invention provides for the use of an aqueous dispersion of particles composed of polymer and finely divided inorganic solid (aqueous composite-particle dispersion) as a binder in elastic coatings, such as paints, more particularly exterior architectural paints, comprising preparing the aqueous composite-particle dispersion by dispersely distributing ethylenically unsaturated monomers in an aqueous medium and carrying out polymerization by means of at least one free-radical polymerization initiator in the presence of at least one dispersely distributed, finely divided inorganic solid having an average particle diameter ≦100 nm and at least one dispersant by the method of free-radically aqueous emulsion polymerization, and using as ethylenically unsaturated monomers a monomer mixture which comprises ethylenically unsaturated monomers A and optionally 0% to ≦10% by weight of an ethylenically unsaturated monomer B containing an epoxide group (epoxide monomer).