Branched polyesters with sulfonate groups can be obtained by reacting components A, B, optionally C, and optionally D to yield branched polyesters, then reacting these branched polyesters with hydrogen sulfite. Component A is at least one α,β-olefinically unsaturated dicarboxylic acid, component B is at least one di- or higher-functional alcohol, optional component C is at least one di- or higher-functional carboxylic acid or hydroxycarboxylic acid without an α,β-olefinically unsaturated bond, and optional component D is at least one compound of formula CH3(—O—CH2—CH2)n—OH. In reacting the branched polyesters with hydrogen sulfite, a molar amount of hydrogen sulfite is at most 95 mol %, based on an amount of α,β-olefinically unsaturated dicarboxylic acid.