When a flash is aligned with a moving object, subjects perceive the flash to lag behind the moving object. Two different models have been proposed to explain this “flash-lag” effect. In the motion extrapolation model, the visual system extrapolates the location of the moving object to counteract neural propagation delays, whereas in the latency difference model, it is hypothesized that moving objects are processed and perceived more quickly than flashed objects. However, recent psychophysical experiments suggest that neither of these interpretations is feasible (Eagleman & Sejnowski, 2000a, 2000b, 2000c), hypothesizing instead that the visual system uses data from the future of an event before committing to an interpretation. We formalize this idea in terms of the statistical framework of optimal smoothing and show that a model based on smoothing accounts for the shape of psychometric curves from a flash-lag experiment involving random reversals of motion direction. The smoothing model demonstrates how the visual system may enhance perceptual accuracy by relying not only on data from the past but also on data collected from the immediate future of an event.