The cyclopean illusion is the apparent lateral shift of stationary stimuli on a visual axis that occurs when vergence changes. This illusion is predictable from the rules of visual direction. There are three stimulus situations reported in the literature, however, in which the illusion does not occur. In the three experiments reported here we examine those stimulus situations. Experiment 1 showed that an afterimage seen on a stimulus moving on the visual axis does not produce the illusion as reported in the literature but an afterimage seen on a screen does. Experiment 2 showed that the illusion occurs for an intermittently presented stimulus in contrast to what has been reported previously. Experiment 3 showed that a monocular stimulus presented against a random-dot background produced the illusion, also in contrast to what has been reported. The results were consistent with the rules of visual direction.