An important role for neurons in the early visual system is to convey information about the structure of visual stimuli. However, neuronal responses show substantial variation across presentations of the same stimulus. In awake monkeys, it has been assumed that a great deal of this variation is related to the scatter in eye position (inducing scatter in the retinal position of the stimulus). Here we investigate the implied consequence of this assumption, i.e., that the scatter variation in eye position degrades the decodability of the neural response. We recorded from 50 complex cells in primary visual cortex of fixating monkeys while different complex stimuli were presented. Three types of retinal shifts were considered: natural scatter in the fixation, systematic fixation point shift, and systematic stimulus position shift. The stimulus pattern accounts for >50% of the response variance, always six times that accounted for by the scatter in eye position during fixation. The retinal location of a stimulus had to be shifted by 10-12 min of arc, an amount almost two times larger than the smallest picture element, before the responses changed systematically. Nonetheless, changes of the stimulus at the single pixel level often gave rise to discriminable responses. Thus complex cells convey information about the spatial structure of a stimulus, independent of rigid stimulus displacements on the order of the receptive field size or smaller.