A pigmented aqueous basecoat material that includes a dimer fatty acid/polyesterdiol reaction product which is preparable by reacting (a) dimer fatty acids with (b) at least one polyesterdiol of the general structural formula (I) where: R is a divalent radical including 2-10 carbon atoms; R1 and R2 are independently straight-chain or branched alkylene radicals having 2-10 carbon atoms; X and Y are independently O, S or NR3, where R3 is hydrogen or an alkyl radical having 1-6 carbon atoms; and m and n are selected accordingly such that the polyesterdiol possesses a number-average molecular weight of 450-2200 g/mol, components (a) and (b) are used in a molar ratio of 0.7/2.3 to 1.3/1.7, and the resulting dimer fatty acid/polyesterdiol reaction product possesses a number-average molecular weight of 1200-5000 g/mol and an acid number