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< of from 0.8 mol/kg to 2 mol/kg, and c)a specific amount of substance of hydroxyl groups, -OH, of from 1 mol/kg to 4 mol/kg, wherein in each case the specific amount of substance is based on the mass of the polyurethane, a process for the preparation thereof, and a method of use thereof.