When the sinusoidal grating of a “Gabor pattern” is drifted, the apparent position of the pattern shifts in the direction of motion [De Valois, R. L., & De Valois, K. K. (1991). Vernier acuity with stationary moving Gabors. Vision Research, 31, 1619–1626]. We investigated the underlying cause of this illusion by determining whether the effect is a consequence of the internal motion shifting the perceived position of the whole pattern, or a consequence of a shift in the perceived location of the centroid (centre of mass) of the Gabor envelope. While each of these two possible distortions can account for a perceived positional offset, they give different predictions for the apparent size of the stimulus. A simple shift in perceived position results in no change in apparent size, while a centroid shift will likely result in either a decrease or an increase in the pattern’s apparent size, depending on whether the trailing or leading edge of the Gabor stimulus is most affected by motion. We examined whether there is a change in the apparent size of Gabor patterns containing a range of grating motion speeds. We found that the perceived size of the pattern increased in the presence of motion as a function of speed, and is thus consistent with a centroid-shift explanation. We verified that this size change is a consequence of an increase in contrast at the leading edge, since the leading edge appears elongated relative to the trailing edge. We furthermore showed that the apparent-position shifts due to motion can be negated by displacing the centroid in the opposite direction to the motion.