The invention relates to aqueous pigment dispersions comprising at least one dispersed pigment, an aqueous carrier and a copolymer prepared by polymerization of at least one macromonomer (1) having a terminal olefinic unsaturation with a mixture of olefinically unsaturated monomers (2), wherein the macromonomer (1) comprises 1a) 5-100% by weight of at least one polymerized acid functional unsaturated monomer, 1b) optionally at least one polymerized hydroxy functional unsaturated monomer, and optionally 1c) at least one further polymerized olefinically unsaturated monomer, and wherein the mixture of olefinically unsaturated monomers (2) comprises 2a) 5-80% by weight of at least one unsaturated vinyl aromatic monomer, 2b) 5-50% by weight of at least one vinyl monomer with at least one polar heterocyclic group with a 5 or 6 membered ring containing at least one ring nitrogen atom which is not connected to a hydrogen atom, and optionally 2c) other olefinically unsaturated monomers.