The invention relates to a method for producing a polymer by means of nitroxyl-controlled polymerisation. According to the invention, a mixture is initiated which contains at least one radically polymerisable monomer and additionally contains at least one initiator, at least one reactive agent that converts at least one portion of the alkoxyamine end groups produced during the radical polymerisation into a non-polymerisable group, and at least one additive that accelerates the hydroxyl-controlled polymerisation and/or the conversion of the alkoxyamine end groups into a non-polymerisable group.