We extended earlier results [J. Opt. Soc. Am. A 16, 2625 (1999)] to examine how the responses of the three postreceptoral mechanisms are combined to subserve discrimination of suprathreshold stimuli. Test thresholds were obtained in the presence of suprathreshold pedestals selected in different quadrants of the red-green/luminance and blue-yellow/luminance planes of cardinal color space. We showed that (1) test threshold was directly proportional to pedestal contrast for pedestal contrasts exceeding five times pedestal contrast threshold, and (2) there were exceptions to this proportionality, notably when the test and pedestal directions were fixed in the cardinal directions. Results support a ratio model of suprathreshold color-luminance discrimination, in which discrimination depends on a ratio of outputs of the postreceptoral mechanisms. We also observed that when test threshold was measured as a function of test color-space direction, masking by the achromatic component of the pedestal was less than that by the chromatic component. In addition, masking by a dark (negative luminance component) pedestal was lower than masking by a light (positive luminance) pedestal of a similar contrast. Our results demonstrated that (1) there is no fundamental difference between discrimination in the isoluminant and in the two chromoluminant cardinal planes, (2) there exists the possibility that discrimination in cardinal directions differs from that in noncardinal (intermediate) directions, and (3) suprathreshold discrimination of luminance differences may be more sensitive than that of chromatic differences for a given suprathreshold pedestal.