A one-piece cable tie, such as an in-line cable tie, includes a hybrid locking mechanism including both a fixed locking wedge and a hinged locking wedge. The hinged locking wedge may be laterally offset from the fixed locking wedge along a longitudinal axis of an internal passageway of the cable tie head. Preferably, the hinged locking wedge is located on a top surface of the passageway while the fixed locking wedge is located on a bottom surface of the passageway. The hinged locking wedge may be located close to the strap ingress. The cable tie is preferably made of Nylon 6.6, yet can achieve both a low thread insertion force and a high loop tensile strength suitable for demanding applications. Maximized strength is achieved through use of multiple teeth on each of the hinged and fixed locking wedges.