Most cortical visual neurons do not respond linearly with contrast. Generally, they show saturated responses to stimuli of high contrast, a feature often characterized by a divisive normalization function. This nonlinearity is generally thought to be useful in focusing the dynamic response range of the neuron on a particular region of contrast space, optimizing contrast gain. Some neurons not only saturate but also supersaturate; at high contrast, the response of the neuron decreases rather than plateaus. Under the contrast gain control theory, these cells would seem to reflect a nonoptimal normalization pool that provides excessive inhibition to the neurons. Since very few data on supersaturation are available, this article examines the frequency with which such neurons occur in macaque visual cortex by considering an extension of the Naka–Rushton equation with the capacity to represent nonmonotonic functions. The prevalence of gain-control theories for saturation has occluded an additional computational function for saturation, namely, in detecting the conjunction of certain features. A saturating nonlinearity is a critical part of the selective detection of compound stimuli over their components. In this role, the existence of saturating contrast response functions might be considered necessary rather than simply optimal.