Accepting the first postulate of the retinex theory of color vision that there are three independent lightness-determining mechanisms (one for long waves, one for middle waves, and one for short waves), each operative with less than a millisecond exposure and each served by its own retinal pigment, a basic task of retinex theory becomes the determination of the nature of these mechanisms. Earlier references proposed several workable algorithms. [Land, E. H. (1959) Proc. Natl. Acad. Sci. USA 45, 115-129; Land, E. H. (1959) Proc. Natl. Acad. Sci. USA 45, 636-644; Land, E. H. (1983) Proc. Natl. Acad. Sci. USA 80, 5163-5169; Land, E. H. & McCann, J. J. (1971) J. Opt. Soc. Am. 61, 1-11; Land, E. H. (1986) Vision Res. 26, 7-21.] The present paper describes a relatively simple alternative technique for the computation of the designator in retinex theory and reports the general operational effectiveness of the new technique, including the competence, not possessed by earlier algorithms, for generating Mach bands.