Dental archwires of single-crystal shape memory alloys, methods of fabrication and apparatus for fabrication. A dental archwire is provided of a hyperelastic, single-crystal shape memory CuAlX alloy, where X is Ni, Mn, Nb, or Be. The dental archwire has a shape-set curved length and either a round diameter of between about 0.013 to about 0.026 inches or a rectangular cross-section with dimensions of between about 0.016 by 0.016 inches and about 0.020 by 0.030 inches.