Estimating depth from binocular disparity is extremely precise, and the cue does not depend on statistical regularities in the environment. Thus, disparity is commonly regarded as the best visual cue for determining 3D layout. But depth from disparity is only precise near where one is looking; it is quite imprecise elsewhere 1–4. Away from fixation, vision resorts to using other depth cues—e.g., linear perspective, familiar size, aerial perspective. But those cues depend on statistical regularities in the environment and are therefore not always reliable 5. Depth from defocus blur relies on fewer assumptions and has the same geometric constraints as disparity 6 but different physiological constraints 7–14. Blur could in principle fill in the parts of visual space where disparity is imprecise 15. We tested this possibility with a depth-discrimination experiment. Disparity was more precise near fixation and blur was indeed more precise away from fixation. When both cues were available, observers relied on the more informative one. Blur appears to play an important, previously unrecognized 16, 17 role in depth perception. Our findings lead to a new hypothesis about the evolution of slit-shaped pupils and have implications for the design and implementation of stereo 3D displays. Display omitted ► Depth from disparity and depth from blur have analogous geometries ► Disparity is very precise near fixation, but blur is more precise elsewhere ► The two cues allow more accurate depth perception than from either cue alone ► Slit pupils cause asymmetric blur, aiding depth discrimination along the ground