An orthodontic brace includes a set of appliances that are connected to respective teeth of the patient. At least some of the appliances include a latch that is operable to release an archwire from the appliance whenever the force exerted by the archwire exceeds a certain value. This value is higher for appliances connected to certain teeth than the value associated with appliances connected to other teeth, in accordance with the particular malocclusion encountered. The brace is constructed to ensure that the goals of the treatment program are carried out in an efficient manner while reducing the likelihood of inadvertent release of the archwire during the course of treatment.