The invention relates to an aqueously dispersible polyurethane having a specific amount of substance of hydroxyl groups, —OH, of at least 0.6 mol/kg, and additionally satisfying at least two of the following conditions: a) a degree of branching measured as specific amount of substance of tertiary and/or quaternary aliphatic carbon atoms of from 0.01 mol/kg to 0.5 mol/kg, b) a specific amount of urea groups >N—CO—N