The present invention relates to a process for producing a polyurethane, comprising at least the following steps (A) bringing at least one polymer polyol into contact with an amount of from 0.1 to 20 mol %, based on the entire amount of polyisocyanate, of at least one first polyisocyanate, in order to obtain a prepolymer which in essence has terminal hydroxy groups, and (B) bringing the prepolymer from step (A) into contact with at least one second polyisocyanate and optionally with further additives, in order to obtain the polyurethane, to a polyurethane obtainable via said process, and also to the use of this polyurethane as cladding in automobiles, coatings, cables, plug connectors, solar modules, foils, moldings, shoe soles and shoe components, balls and ball components, rollers, fibers, profiles, laminates and wiper blades, hoses, cable plugs, bellows, drag cables, cable sheathing, gaskets, nonwoven fabrics, drive belts, or damping elements.