An aesthetic, partially removable orthodontic appliance is described, including a polymeric body that conforms to the lingual soft tissue and at least one wire member extending from the polymeric body. Each wire member releasably engages with a respective anchor that is, in turn, connected to the lingual surface of a respective tooth when the polymeric body is moved in a generally gingival direction into abutting relationship with the lingual soft tissue. Other features of the appliance include self-guiding magnetic couplings and couplings based on interlocking mechanical structures that provide releasable engagement between the removable section and the anchors, as well as related methods for making and using the same.