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Binocular depth perception is an important mechanism to segregate the visual scene for mapping relevant objects in our environment. Convergent evidence from psychophysical and neurophysiological studies have revealed asymmetries between the processing of near (crossed) and far (uncrossed) binocular disparities. The aim of the present study was to test if near or far objects are processed faster and with higher contrast sensitivity in the visual system. We therefore measured the relationship between binocular disparity and simple reaction time (RT) as well as contrast gain based on the contrast-RT function in young healthy adults. RTs were measured to suddenly appearing cyclopean target stimuli, which were checkerboard patterns encoded by depth in dynamic random dot stereograms (DRDS). The DRDS technique allowed us to selectively study the stereoscopic processing system by eliminating all monocular cues. The results showed that disparity and contrast had significant effects on RTs. RTs as a function of disparity followed a U-shaped tuning curve indicating an optimum at around 15 arc min, where RTs were minimal. Surprisingly, the disparity tuning of RT was much less pronounced for far disparities. At the optimal disparity, we measured advantages of about 80 ms and 30 ms for near disparities at low (10%) and high (90%) contrasts, respectively. High contrast always reduced RTs as well as the disparity dependent differences. Furthermore, RT-based contrast gains were higher for near disparities in the range of disparities where RTs were the shortest. These results show that the sensitivity of the human visual system is biased for near versus far disparities and near stimuli can result in faster motor responses, probably because they bear higher biological relevance.