A polymer dispersion is produced by polymerization of at least two different ethylenically unsaturated monomers in at least first and second stages. The polymer produced in the first stage comprises 25 to 60% by weight of the total monomer composition and has a uniform glass transition temperature from −30° C. to 0° C. The polymer produced in the second stage comprises 40 to 75% by weight of the total monomer composition and has a variable monomer composition such that the second stage polymer has a non-uniform glass transition temperature which varies between a first value from −30° to +10° C. and second value of at least +70° C. Any polymer produced in further polymerization stages comprises no more than 10% by weight of the total monomer composition and the glass transition temperature of the hypothetical uniform copolymer produced by the total monomer composition is in the range from 0° C. to 25° C.