Non-sliding orthodontic appliances may include an archwire having male fasteners for locking in place with brackets in a non-sliding manner and interproximal loops for exerting forces on the brackets. Appropriate forces may be calculated according to vectors between initial and ideal tooth positions. The brackets may be transferred to a patient's teeth using indirect bonding trays which contain slots for holding and aligning each bracket. The trays may include integrated handles for facilitating handling, may be sectioned into smaller pieces for easier application, and/or may be labeled for facilitating proper registration. Superposition of a digital placement plan and clinical model after bonding may illustrate the accuracy of bracket placement. The archwire may comprise atraumatic ends to avoid patient discomfort. A color registration system can be used to facilitate the attachment of the archwire to the brackets. The archwire may be locked into place with the brackets using crimpable stops.