J. W. Peirce (2007, p. 1) has proposed that saturating contrast-response functions in V1 and V2 may form "a critical part of the selective detection of compound stimuli over their components" and that supersaturating (non-monotonic) functions allow even greater conjunction selectivity. Here, we argue that saturating and supersaturating contrast-response functions cannot be exploited by conjunction detectors in the way that Peirce proposes. First, the advantage of these functions only applies to conjunctions with components of lower contrast than the equivalent non-conjunction stimulus, e.g., plaids (conjunctions) vs. gratings (non-conjunctions); most types of conjunction do not have this property. Second, in many experiments, conjunction and non-conjunction components have identical contrast, sampling the contrast-response function at a single point, so the function's shape is irrelevant. Third, Peirce considered only maximum-contrast stimuli, whereas contrasts in natural scenes are low, corresponding to a contrast-response function's expansive region; we show that, for naturally occurring contrasts, Peirce's plaid detector would generally respond more weakly to plaids than to gratings. We also reassess Peirce's claim that supersaturating contrast-response functions are suboptimal for contrast coding; we argue that supersaturation improves contrast coding, and that the multiplicity of supersaturation levels reflects varying trade-offs between contrast coding and coding of other features.