Abstract: Orthodontic brackets having tubular passages are bonded to at least six teeth in an upper or lower human dental arch, including at least two teeth other than molars, and a superflexible archwire is extended through all of the passages. The orthodontic brackets are non-metallic thin veneer bodies having tubular passages for receiving the archwire. Custom veneer bodies are fabricated using information obtained from a model or a sectioned model of a patient's dental arch, or from digital mapping of the patient's tooth surfaces or the facsimile tooth surfaces in the model. The orientation of each tubular passage in each bracket depends upon the desired final position of each tooth, and upon the degree of torque, tip and angulation required for achieving such position. Contrary to the prior practice of making orthodontic brackets as small as possible, the veneer bodies have a large bonding surface area that covers much of a tooth facial surface and corresponds with the facial surface shape of the tooth.