The need for affordable and sustainable ophthalmic systems for measurement and correction of refraction is well recognized. Power-adjustable spectacles based on the Alvarez principle (transversal lateral movement of two lenses) have emerged as an innovative technology for this purpose. Within this framework, our aim is to design a new power-adjustable sphero-cylindrical refractor. The system is comprised of two lenses and three independent lateral movements. The lenses have a planar and a third-degree polynomial surface. They are arranged with their planar surfaces in contact, so that the incoming light is only refracted by two surfaces. First, we present the theory of such a system. Second, we propose an optical design methodology. Third, we provide a design example capable of measuring sphere powers ranging from −5.00 D to +5.00 D and cross-cylinders from −2.00 D to 2.00 D. Finally, a prototype of the lenses was manufactured using free-form machining.