A method comprising: receiving, with a computer system (70, 80), a digital representation of a three-dimensional tooth structure of a patient, the tooth structure providing initial positions of one or more teeth of the patient; determining, with the computer system (70, 80), dimensions and shapes of a removable dental appliance (100; 101; 150; 160; 400; 500; 600; 700; 800) for the patient, the dimensions and shapes of the removable dental appliance (100; 101; 150; 160; 400; 500; 600; 700; 800) being configured to reposition the one or more teeth of the patient from their initial positions to adjusted positions when the removable dental appliance (100; 101; 150; 160; 400; 500; 600; 700; 800) is worn by the patient; and transmitting, with the computer system (70, 80), a representation of the removable dental appliance (100; 101; 150; 160; 400; 500; 600; 700; 800) to a computer-aided manufacturing system, wherein the removable dental appliance (100; 101; 150; 160; 400; 500; 600; 700; 800) comprises an appliance body (102; 402; 502; 602; 702; 802) configured to surround two or more teeth of the patient, wherein the appliance body (102; 402; 502; 602; 702; 802) includes: a facial portion (106; 406; 506; 606; 706; 806) configured to register with facial sides of the surrounded teeth; and a lingual portion (104; 404; 504; 604; 704; 804) configured to register with lingual sides of the surrounded teeth, wherein the appliance body (102; 402; 502; 602; 702; 802) is configured such that occlusal surfaces of the surrounded teeth of the patient are exposed when the removable dental appliance (100; 101; 150; 160; 400; 500; 600; 700; 800) is worn by the patient, and wherein determining, with the computer system (70, 80), dimensions and shapes of the removable dental appliance (100; 101; 150; 160; 400; 500; 600; 700; 800) includes selecting thicknesses of the facial portion (106; 406; 506; 606; 706; 806) and the lingual portion (104; 404; 504; 604; 704; 804) of the appliance body (102; 402; 502; 602; 702; 802) in order to provide a stiffness suitable to reposition the one or more teeth of the patient from their initial positions to adjusted positions when the removable dental appliance (100; 101; 150; 160; 400; 500; 600; 700; 800) is worn by the patient. receiving, with a computer system (70, 80), a digital representation of a three-dimensional tooth structure of a patient, the tooth structure providing initial positions of one or more teeth of the patient; determining, with the computer system (70, 80), dimensions and shapes of a removable dental appliance (100; 101; 150; 160; 400; 500; 600; 700; 800) for the patient, the dimensions and shapes of the removable dental appliance (100; 101; 150; 160; 400; 500; 600; 700; 800) being configured to reposition the one or more teeth of the patient from their initial positions to adjusted positions when the removable dental appliance (100; 101; 150; 160; 400; 500; 600; 700; 800) is worn by the patient; and transmitting, with the computer system (70, 80), a representation of the removable dental appliance (100; 101; 150; 160; 400; 500; 600; 700; 800) to a computer-aided manufacturing system, wherein the removable dental appliance (100; 101; 150; 160; 400; 500; 600; 700; 800) comprises an appliance body (102; 402; 502; 602; 702; 802) configured to surround two or more teeth of the patient, wherein the appliance body (102; 402; 502; 602; 702; 802) includes: a facial portion (106; 406; 506; 606; 706; 806) configured to register with facial sides of the surrounded teeth; and a lingual portion (104; 404; 504; 604; 704; 804) configured to register with lingual sides of the surrounded teeth, wherein the appliance body (102; 402; 502; 602; 702; 802) is configured such that occlusal surfaces of the surrounded teeth of the patient are exposed when the removable dental appliance (100; 101; 150; 160; 400; 500; 600; 700; 800) is worn by the patient, and a facial portion (106; 406; 506; 606; 706; 806) configured to register with facial sides of the surrounded teeth; and a lingual portion (104; 404; 504; 604; 704; 804) configured to register with lingual sides of the surrounded teeth, wherein the appliance body (102; 402; 502; 602; 702; 802) is configured such that occlusal surfaces of the surrounded teeth of the patient are exposed when the removable dental appliance (100; 101; 150; 160; 400; 500; 600; 700; 800) is worn by the patient, and wherein determining, with the computer system (70, 80), dimensions and shapes of the removable dental appliance (100; 101; 150; 160; 400; 500; 600; 700; 800) includes selecting thicknesses of the facial portion (106; 406; 506; 606; 706; 806) and the lingual portion (104; 404; 504; 604; 704; 804) of the appliance body (102; 402; 502; 602; 702; 802) in order to provide a stiffness suitable to reposition the one or more teeth of the patient from their initial positions to adjusted positions when the removable dental appliance (100; 101; 150; 160; 400; 500; 600; 700; 800) is worn by the patient.