M. Singh and B. L. Anderson proposed a perceptual theory of achromatic transparency in which the perceived transmittance of a perceived transparent filter is determined by the ratio of the Michelson contrast seen in the region of transparency to that of the background seen directly. Subsequently, B. L. Anderson, M. Singh, and J. Meng proposed that Michelson contrast should be replaced by perceived contrast in this theory. However, their experimental stimuli were nongeneric (i.e., special cases), and their observers had little choice in their matching strategy. Here, the author shows that both of their ratio-of-contrasts theories are incorrect and that problems with their theoretical analyses and experimental designs led them to conclude that mean luminance does not affect perceived transmittance when contrast is held constant. The author also shows that B. L. Anderson's (2003) transmittance anchoring principle is not valid when a transparent surface is perceived to penetrate rather than overlay another surface. Finally, the author shows that M. Singh's (2004) theoretical proof that the ratio-of-Michelson-contrasts theory accurately predicts lightness matching through transparency is incorrect.