Rudd and Zemach analyzed brightness/lightness matches performed with disk/annulus stimuli under four contrast polarity conditions, in which the disk was either a luminance increment or decrement with respect to the annulus, and the annulus was either an increment or decrement with respect to the background. In all four cases, the disk brightness—measured by the luminance of a matching disk—exhibited a parabolic dependence on the annulus luminance when plotted on a log-log scale. Rudd further showed that the shape of this parabolic relationship can be influenced by instructions to match the disk’s brightness (perceived luminance), brightness contrast (perceived disk/annulus luminance ratio), or lightness (perceived reflectance) under different assumptions about the illumination. Here, I compare the results of those experiments to results of other, recent, experiments in which the match disk used to measure the target disk appearance was not surrounded by an annulus. I model the entire body of data with a neural model involving edge integration and contrast gain control in which top-down influences controlling the weights given to edges in the edge integration process act either before or after the contrast gain control stage of the model, depending on the stimulus configuration and the observer’s assumptions about the nature of the illumination.