The contrast threshold for detecting a low frequency test grating in the presence of a contrast-modulated high frequency masker is heavily dependent upon the phase relations between the gratings: test stimuli in + or - cosine phase are much more detectable than those in + or -sine phase. The present study tests a new hypothesis of these and related phenomena. It is based on the report by Derrington (1987) that recordings from cat geniculate on-center and off-center X-cells exhibit significant point nonlinearities. The major empirical finding of this study is that for highly practiced observers, sine-phase test stimuli and cosine-phase test stimuli are similar in two important respects: (1) there exist phase uncertainty effects; that is, detection thresholds for test stimuli differing in phase by 180 degrees are elevated when they are intermixed within the same block of trials, rather than being presented in separate blocks; (2) phase identification thresholds for test stimuli differing in phase by 180 degrees are the same as their detection thresholds. The new nonlinearity hypothesis cannot account for the results obtained with sine-phase test stimuli, though it gives a better account of the results with cosine-phase stimuli than does the early nonlinearity hypothesis which was tested and rejected by Nachmias and Rogowitz (1983).