The present invention relates to a solventborne, pigmented coating composition having a solids fraction of at least 35%, which comprises, based on the total amount of the coating composition, 0.1 to 1.5 wt % of at least one copolymer (A), where the copolymer (A) is obtainable by copolymerization of a mixture of olefinically unsaturated monomers (a) in at least one organic solvent, the mixture of monomers (a) to be polymerized consists of (a1) 10 to 60 mol % of at least one monomer of the formula (I) below where R1═C1 to C4 alkoxy, R2═C1 to C4 alkyl, and m=0 to 2, and also (a2) 40 to 90 mol % of at least one further olefinically unsaturated monomer, and the copolymer (A) possesses a glass transition temperature Tg of at least −30° C. The present invention also relates to a method for producing a multicoat paint system using the coating composition, and to the multicoat paint systems themselves.