During the winding of coils with a non-circular shape the wire length necessary varies periodically for a trouble-free winding per unit of time. At a high winding rotational speed and unsatisfactory side ratios relative to the coil being wound, the periodic change in the required wire length is so large that with known wire brakes there is no adequate winding quality with a concurrent protective handling of the wire. These opposite goals are reached through the invention with the aid of a controllable wire brake which essentially consists of a plurality of brake strands wound about the wire in a single layer.