In asymmetric lightness matching tasks, observers sometimes report that they cannot achieve satisfactory matches between achromatic surfaces under different neutral illuminants. The surfaces appear different, yet no further adjustment of either surface improves the match. There are evident difficulties in interpreting data from a task that the observer cannot always do, and these difficulties likely affect the interpretation of a large number of previous studies. We investigated, as an alternative to asymmetric matching, the direct use of proximity judgments in the study of surface lightness perception. We asked observers to rate the perceived dissimilarity of pairs of achromatic surfaces that were placed in identical scenes and viewed under different neutral illuminants. We develop a parametric model that accurately predicts perceived dissimilarity in terms of physical light intensities and surface albedos. The parameters of this model are readily interpretable. In particular, the ratio of the influence of changes in illuminant intensity and changes in surface albedo is a measure of the extent to which the observer discounts the illuminant. Asymmetric lightness matching can be interpreted as an unachievable limiting case of proximity judgment.