The direction illusion is the phenomenal exaggeration of the angle between the drift directions, typically, of two superimposed sets of random dots. The direction illusion is commonly attributed to mutual inhibition between direction-selective cell populations (distribution-shift model). A second explanation attributes the direction illusion to the differential processing of relative and non-relative motion components (differential processing model). Our first experiment demonstrates that, as predicted by the differential processing model, a static line can invoke a misperception of direction in a single set of dots - a phenomenon we refer to as the statically-induced direction illusion. In a second experiment, we find that the orientation of a static line can also influence the size of the conventional direction illusion. A third experiment eliminates the possibility that these results can be explained by the presence of motion streaks. While the results of these experiments are in agreement with the predictions made by the differential processing model, they pose serious problems for the distribution-shift account of shifts in perceived direction.