A process for preparing a randomly branched copolymer, by reacting the components (a) 10-98.9 mol % of at least one acrylic ester of a straight-chain, branched or cyclic C1-C22-alkyl monoalcohol, (b) 0.1-10 mol % of at least one polyethylenically unsaturated monomer and (c) optionally one or more monoethylenically unsaturated monomers other than acrylic esters of straight-chain, branched or cyclic C1-C22-alkyl monoalcohols and other than compounds of the formula (I), in the presence of (d) 1-10 mol % of at least one compound of the formula (I) H3C—CRaRc—CH2—CRa—CH2 (I) where Ra, Rb are each independently aryl, CN or COOR1 where R1═H, alkyl, aryl or aralkyl, and Rc=alkyl, aryl or aralkyl, and is the presence of at least one initiator of free-radical polymerization in a free-radical polymerization, where the stated molar proportions of components (a), (b), (c) and (d) add up to 100 mol %, and where the molar proportion of component (b) does not exceed the molar proportion of component (d), Copolymers obtainable by the process and use thereof as levelling agents in coating substances.