Recent reports have noted that dots that move obliquely upwards behind vertical parallels appear to emerge too high (kinetic illusion, or KI), and that alternating the left and right halves of the Poggendorff illusion increases alignment error. However, when the parallels are omitted, the KI remains large but the alternating line illusion is reduced markedly. In three experiments, this difference was not replicated: both successive effects were larger than static illusions, both increased with interstimulus interval, and introducing parallels added a constant to all three effects. Fixation versus pursuit made no difference. The data suggested that a simple eye-movement account of the KI was unlikely to be tenable. Deterioration of memory for spatial location of the first stimulus was considered a possible contributor.