Abstract: Composite arrow or crossbow bolt shafts have a hollow core, where the inner diameter of the shafts vary along the length of the shaft, but the outer diameter of the shafts remains constant. The hollow inner core may vary gradually in size along the length of the shaft, or it may vary in discrete stepped portions so that the shaft is more hollow in some portions in comparison to others. The hollow composite shafts may be manufactured by wrapping a tapered or stepped inner mandrel with fibers of a composite material and curing that composite material, or by triaxially braiding composite fibers around a tapered or stepped inner mandrel before curing those composite fibers.