When visual information is provided in addition to input from other sensory systems, normal body sway can be attenuated by about 50%. The essential visual cue is retinal target displacement, which increases as eye-target distance is reduced. As a result, both lateral and anterior/posterior (A-P) sway decrease as eye/target distance decreases. We have investigated the geometrical basis of lateral and fore-aft sway detection by vision, the latter provided by detection of change in disparity of the visual axis of both eyes and change in target size. Using known movement detection thresholds the largest possible distance for visual stabilization of posture can be calculated to be 34 m for lateral sway, and for fore-aft sway 1.50 m for change in disparity and 3.20 m for change in size. Visual stimuli were designed to selectively stabilize fore-aft sway either by change in size or by change in disparity. The experiments revealed that the theoretical prediction overestimates the efficacy of visual stabilization of lateral sway and underestimates the efficacy of fore-aft sway stabilization. It is proposed that microoscillations of the eye increase the threshold for detection of retinal target displacements, leading to less efficient lateral sway stabilization than expected, and that the threshold for detection of self motion in the A-P direction is lower than the threshold for object motion detection used in the calculations, leading to more efficient stabilization of A-P sway.