Liu, Tyler, and Schor (1992 Vision Research 32 1471-1479) reported the surprising finding that dichoptically presented orthogonal sine-wave gratings do not always produce binocular rivalry. Gratings of high spatial frequency, and especially of low contrast, fuse to produce a stable percept of a dichoptic plaid. Using a somewhat different perceptual task, we replicated those findings and extended them. The probability of a plaid percept is higher for square-wave gratings than for sine-wave gratings, and higher still for rectangular-wave gratings with high duty cycles (with very thin light or dark bars). Experiments were conducted to test whether this duty-cycle effect was due to changes in overall luminance, or in the size of the regions of luminance congruity (which may reduce the probability of rivalry), but no such effects could account for the results. The presence of locally conflicting contour information in the two eyes was shown to be an important determinant of rivalry onset, but, since removing such regions did not eliminate rivalry, other factors also have a role to play. The spatial frequency composition of the gratings is one such factor which is consistent with all of the findings we report.