The present invention relates to a method and apparatus for reducing catenary during winding of a fiber bundle which includes a plurality of fiber strands into a wound package. The method includes: applying substantially equal tension to each of a plurality of fiber strands; gathering the strands to form a bundle; advancing the bundle at a predetermined speed and tension toward a winding device; measuring the tension of the bundle; adjusting the tension of the bundle by adjusting the speed at which the bundle is advanced, such that (1) the speed of advancement of the bundle is increased when the measured tension of the bundle exceeds a predetermined value and (2) the speed of advancement of the bundle is decreased when the measured tension of the bundle is less than a second predetermined value; and winding the bundle to form a wound package. The apparatus includes a frame; a plurality of fiber strand supply packages; a plurality of tensioning devices for applying substantially equal tension to each of the fiber strands; a gathering device for gathering the fiber strands into a fiber bundle; a feed device for advancing the fiber bundle at a predetermined speed to a winding device; a tension sensing device for determining the tension in the bundle and providing a signal to a feed device controller which adjusts the speed of the feed device in response to the signal from the tension sensing device; and a winding device.