The visual system has a remarkable ability to reconstruct 3-D structure from moving 2-D features. The processing of structure from motion is generally thought to consist of two stages. First, the direction and speed of features is measured (2-D velocity measurement) and, second, 3-D structure is reconstructed from the measured 2-D velocities (3-D structure recovery). Most models have assumed that these stages occur in a bottom-up fashion. Here, however, we present evidence that the 3-D structure-recovery stage influences the 2-D velocity-measurement stage. We developed a stimulus in which two perceptual modes of motion correspondence (one-way translation versus oscillation), and two perceptual modes of 3-D surface structure (flat surface versus cylinder) could be achieved. We found that the likelihood of perceiving both one-way motion and cylindrical structure increased in similar ways with increasing frame duration. In subsequent experiments we found, first, that a higher likelihood of perceiving one-way motion did not affect the likelihood of perceiving cylindrical structure; and, second, that a higher likelihood of perceiving cylindrical structure increased the likelihood of perceiving one-way motion. These results suggest that the higher, 3-D structure-recovery stage may influence the lower, 2-D motion-correspondence stage. This result is not in accordance with most computational models that assume that there is only one-way, feedforward information processing from the 2-D velocity (energy)-measurement stage to the 3-D structure-recovery stage. Perhaps, one of the roles of feedback processing is to seek consensus of the information processed in different stages.