It has been hypothesized that lightness is computed in a series of stages involving: (1) extraction of local contrast or luminance ratios at borders; (2) edge integration, to combine contrast or luminance ratios across space; and (3) anchoring, to relate the relative lightness scale computed in Stage 2 to the scale of real-world reflectances. The results of several past experiments have been interpreted as supporting the highest luminance anchoring rule, which states that the highest luminance in a scene always appears white. We have previously proposed a quantitative model of achromatic color computation based on a distance-dependent edge integration mechanism. In the case of two disks surrounded by lower luminance rings, these two theories—highest luminance anchoring and distance-dependent edge integration—make different predictions regarding the luminance of a matching disk required to for an achromatic color match to a test disk of fixed luminance. The highest luminance rule predicts that luminance of the ring surrounding the test should make no difference, whereas the edge integration model predicts that increasing the surround luminance should reduce the luminance required for a match. The two theories were tested against one another in two experiments. The results of both experiments support the edge integration model over the highest luminance rule.