An orthodontic appliance may include an archwire and multiple orthodontic brackets. The archwire may fit within a human mouth and contain multiple male connectors. Each orthodontic bracket may have a configuration that facilitates attaching the orthodontic bracket to a single tooth. Each orthodontic bracket may allow one of the male connectors to be locked into the orthodontic bracket with a snapping action. The male connector may be unable to slide with respect to the orthodontic bracket after being locked in the orthodontic bracket. A manual unlocking action may allow the male connector to disengage from the orthodontic bracket.