Several studies have shown that the perceived position of a briefly presented stimulus can be displaced by nearby motion or by eye movements. We examined whether attentive tracking can also modulate the perceived position of flashed static objects when eye movements and low-level motion are controlled. Observers attentively tracked two target bars 180 degrees apart on a rotating, 12-spoke radial grating and judged the alignment of two flashes that were briefly presented, one on each side of the grating. Because of the symmetry of the 12-spoke grating, test flashes could be timed so that the rotating grating was always aligned to a standard orientation at the time of the test, while the tracked bars themselves, being only two of the 12 spokes, could probe locations that differed by multiples of 30 degrees ahead of, aligned with, or behind, the test bars. Despite the physical identity of the stimulus in each test--same orientation, same motion--the perceived position of the two flashes strongly depended on the locus of attention: when the test flashes were presented ahead of the tracked bars, a large position shift in the direction of the grating's motion was seen. If they were presented behind the tracked bars, the illusory displacement was reduced or slightly reversed. These effects of attention led us to suggest an attentional model of position distortions that links the effects seen for motion and for eye movements.