The present invention provides an insert, or sleeve, for use in a baseball or softball bat that improves power transfer from the bat to the batted ball. The insert includes multiple layers of composite material. Most of the layers include fibers that are directed substantially circumferentially about the insert. Since the largest component of stress within the insert produced by an impact with a ball is typically compressive hoop stress, which is directed substantially circumferentially about the insert, the circumferential layers are able to withstand the majority of the stress produced by an impact. The insert also includes non-circumferential layers that serve to hold the circumferential layers together and withstand the smaller stresses in other directions. Because the insert has its greatest strength in substantially the circumferential direction, less material is required to withstand the stress produced by repeated impacts with a ball. The insert also produces a bat having superior impact response characteristics.