A cable tensioner for an industrial door helps keep a cable neatly wrapped on its take-up drum. In some embodiments, the tensioner functions in a first mode during normal door operation, and operates in a second mode when the tension in the cable decreases to a predetermined low level. When operating in the second mode, the tensioner is able to take up slack in a cable that supports a door member, such as a door panel or a deadweight that counteracts the door panel's weight. The tensioner includes a shock absorber that resists a reaction force pulling on the tensioner when the tensioner is in the second mode. The tensioner may be adapted for use on various doors including, but not limited to, sectional doors, roll-up doors, high-lift doors, horizontally storing doors, vertically storing doors, and various combinations thereof.