Appliances are made using a dental mold representing a patient's dental configuration. In particular, thermoformable plastic positioning appliances which fit over the patient's teeth may be formed over a three-dimensional mold of the patient's dentition. An apparatus and methods which employ a manipulable or reconfigurable mold to model patient dentition and gingiva at each stage of treatment. The apparatus and methods are particularly useful for performing midcourse corrections during orthodontic procedures using a plurality of such appliances in sequence.