Abstract: An orthodontic appliance is rigid to avoid significant flexing due to therapeutic magnetic forces. The orthodontic appliance is magnetically mountable on the lingual or palatal side of teeth of a patient. Magnetic or magnetizable targets are mounted only on the lingual or palatal side of the patient's teeth. Orthodontic components are obscured from view behind the patient's teeth. Orthodontic correction is provided with improved esthetics. Magnets and/or targets can be of custom, designed or selected shapes, including non-planar shapes, to provide a desired force vector.