Incompatible patterns viewed by each of the two eyes can provoke binocular rivalry, a competition of perception. Levelt’s first law predicts that a highly visible stimulus will predominate over a less visible stimulus during binocular rivalry. In a behavioural study, we made a counterintuitive observation: high visibility patterns do not always predominate over low visibility patterns. Our results show that none of Levelt’s binocular rivalry laws hold when luminance-modulated (LM) patterns compete with contrast-modulated (CM) patterns. We discuss visual saliency, asymmetric feedback, and a combination of both as potential mechanisms to explain the CM versus LM findings. Competing orthogonal LM stimuli do follow Levelt’s laws, whereas only the first two laws hold for competing CM stimuli. The current results provide strong psychophysical evidence for the existence of separate processing stages for LM and CM stimuli.