The traditional clinical designation of spherocylindrical power unambiguously specifies the refractive properties of a thin lens or refractive surface. This representation of dioptric power is not, however, optimum in mathematical terms, as is apparent when, for example, two spherocylindrical lens powers are added. Alternative systems have been described which are not subject to this same type of difficulty, and the essential feature of these other systems is that spherocylindrical power is defined in terms of a three-dimensional dioptric space in which the axes are usually orthogonal. The advantages of this orthogonality can be exploited in the practice of clinical refraction, provided lens powers in these three dimensions can be physically implemented. Systems using these characteristics have been introduced in the past, but the clinical community has not adopted them on a widespread basis. However, systems which take advantages of these features do have unique advantages relative to traditional clinical refraction procedures. These characteristics, and refractive procedures which exploit their advantages, are described.