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Properly perceived stereo display is often assumed to be vital in augmented reality (AR) displays used for close distances, echoing the general understanding from the perception literature. However, the accuracy of the perception of stereo in head-worn AR displays has not been studied greatly. We conducted a user study to elicit the precision of stereo perception in AR and its dependency on the size and contrast of the stimulus. We found a strong effect of contrast on the disparity users desired to make a virtual target verge at the distance of a real reference object. We also found that whether the target began behind or in front of the reference in a method of adjustments protocol made a significant difference. The mean disparity in the rendering that users preferred had a strong linear relationship with their IPD. We present our results and infer stereoacuity thresholds.