There has been a long-standing debate about the mechanisms underlying the perception of stereoscopic depth and the computation of the relative disparities that it relies on. Relative disparities between visual objects could be computed in two ways: (a) using the difference in the object's absolute disparities (Hypothesis 1) or (b) using relative disparities based on the differences in the monocular separations between objects (Hypothesis 2). To differentiate between these hypotheses, we measured stereoscopic discrimination thresholds for lines with different absolute and relative disparities. Participants were asked to judge the depth of two lines presented at the same distance from the fixation plane (absolute disparity) or the depth between two lines presented at different distances (relative disparity). We used a single stimulus method involving a unique memory component for both conditions, and no extraneous references were available. We also measured vergence noise using Nonius lines. Stereo thresholds were substantially worse for absolute disparities than for relative disparities, and the difference could not be explained by vergence noise. We attribute this difference to an absence of conscious readout of absolute disparities, termed the absolute disparity anomaly. We further show that the pattern of correlations between vergence noise and absolute and relative disparity acuities can be explained jointly by the existence of the absolute disparity anomaly and by the assumption that relative disparity information is computed from absolute disparities (Hypothesis 1).