Many current psychophysical models propose that visual processing in cortex is hierarchical, with nonlinearities sandwiched between linear stages of processing. In earlier publications, we proposed a model of this type to account for masking effects found with spatial frequency and orientation discriminations. Our model includes two nonlinear mechanisms that regulate contrast sensitivity in early cortical mechanisms. The first is a local within-pathway nonlinearity that accelerates at low contrasts but is compressive at high. The second is a pooled nonlinear gain control process that operates over a broad range of neurons with different tuning characteristics. Here, we test predictions of the model for spatial frequency discriminations. The model predicts that at low contrasts, adding a grating mask oriented parallel to test gratings will improve discrimination performance via operation of the within-pathway nonlinearity, analogous to the "dipper effect" found with contrast discriminations. Adding an orthogonally oriented mask is predicted to have no effect at low contrasts, where pooled gain control processes contribute little to performance. At high contrasts, the model predicts that performance will asymptote and become independent of contrast with either parallel or orthogonal masks. The results confirm model predictions.