Simple cells in cat striate cortex are selective for spatial frequency. It is widely believed that this selectivity arises simply because of the way in which the neurons sum inputs from the lateral geniculate nucleus. Alternate models, however, advocate the need for frequency-specific inhibitory mechanisms to refine the spatial frequency selectivity. Indeed, simple cell responses are often suppressed by superimposing stimuli with spatial frequencies that flank the neuron's preferred spatial frequency. In this article, we compare two models of simple cell responses head-to-head. One of these models, the flanking-suppression model, includes an inhibitory mechanism that is specific to frequencies that flank the neuron's preferred spatial frequency. The other model, the nonspecific-suppression model, includes a suppressive mechanism that is very broadly tuned for spatial frequency. Both models also include a rectification nonlinearity and both may include an additional accelerating (e.g., squaring) output nonlinearity. We demonstrate that both models can be consistent with the apparent flanking suppression. However, based on other experimental results, we argue that the nonspecific-suppression model is more plausible. We conclude that the suppression is probably broadly tuned for spatial frequency and that the apparent flanking suppression is actually due to distortions introduced by an accelerating output nonlinearity.