An orthodontic system comprises a prefabricated attachment applied to the labial or lingual side (or both) of one or more teeth, and a set of clear aligners. The prefabricated attachment comprise a base member sized and shaped to cover substantially the entire surface of the tooth to which it is attached, which provides a large adhesive surface area and hence superior adhesion. One or more attachments—sized and shaped smaller than the base member, and formed of a harder material—are affixed to the base member. The attachments, which may assume a wide variety of shapes, provide superior frictional fit to the aligner, thus increasing the amount of corrective force the aligner can apply to the teeth. In some embodiments, the attachments may have an undercut portion an aligner may be formed to have a corresponding protrusion mating to the undercut, providing a firmer grip between the aligner and the tooth. In some embodiments, the attachments may include a passage operative to accept a pin having a feature such as a hook or eye, to which a wire or elastic band may be attached to apply additional corrective force to the tooth.