The study reported here was undertaken in an attempt to contribute, from a theoretical standpoint, to the knowledge and understanding of optimum force theory, particularly as it may be relevant to canine retraction. The following statements are derived from my analysis of the applicable published literature and the results of the present investigation: 1. This study lends support to the beliefs, from the findings of previous investigations, 20, 22 that the center of rotation for simple tipping is three tenths to four tenths of the distance from the root apex to the alveolar crest and that the center of resistance is at approximately midroot for the single-rooted tooth. 2. For a given distal driving force, increasing the countertipping couple from zero causes the center of rotation to "move" from a point near the apical end of the middle third of the root to the root apex and then to infinity. That is, the couple to be developed by the appliance to produce crown movement is smaller than required for bodily movement. Also, increasing the rotational stiffness of a canine-retraction appliance will result in greater inherent potential for canine root control and a greater probability of achieving bodily movement. 3. In a specific orthodontic case, an average periodontal stress value (active force divided by root area) can be used as a basis of comparison of suggested active force magnitudes among several single-rooted teeth having different root surface areas, provided all teeth are to experience the same form of displacement (for example, bodily movement). Similarly, differences in average stress magnitudes developed in the periodontium, rather than differences in root surface areas, are actually the basis for the differential force theory. 4. Clinical studies have suggested that the size of active force for bodily movement or root movement of a given tooth be two to three times that employed in simple tipping of the same tooth. Induced stress levels in the periodontium, especially at the root apex and alveolar crest locations, can be related to suggested magnitudes of aplied crown force components.