Spatial projection and temporal integration are two prominent theories of visual localization for moving stimuli which gain most of their explanatory power from a single process. Spatial projection theories posit that a moving stimulus' perceived position is projected forwards in order to compensate for processing delays (Eagleman & Sejnowski, 2007; Nijhawan, 2008). Temporal integration theories (Krekelberg & Lappe, 2000) suggest that an averaging over positions occupied by the moving stimulus for a period of time is the dominant process underlying perception of position. We found that when magnocellular (M) pathway processing was reduced, there were opposite effects on localization judgments when a smooth, continuous trajectory was used, compared to when the moving object suddenly appeared, or suddenly reversed direction. The flash-lag illusion was decreased for the continuous trajectory, but increased for the onset and reversal trajectories. This cross-over interaction necessitates processes additional to those proposed by either the spatial projection or temporal integration theories in order to explain the perception of the position of moving stimuli across all our conditions. Differentiating our onset trajectory conditions from a Fr诨lich illusion, in a second experiment, we found a null Fr诨lich illusion under normal luminance-defined conditions, significantly smaller than the corresponding flash-lag illusion, but significantly increased when M processing was reduced. Our data are most readily accounted for by Kirschfeld and Kammer's (1999) backward-inhibition and focal attention theory.