This paper describes an evaluation of the capability of two tests of vision, stereoacuity and fusion recovery range, to predict depth discrimination performance for subjects using a hyperstereoscopic display system. For the hyperstereo performance evaluation, 14 subjects completed a depth discrimination task presented at multiple positions and depths in a remote vision system (RVS) simulation similar to that used by air refueling operators on the KC-46 aircraft. Prior to performing the hyperstereo task, each subject completed automated tests of stereoacuity and binocular fusion recovery range. Evaluation results indicate that both stereoacuity (R2 = 0.64) and recovery range (R2 = 0.45) reliably predict (p ≤ 0.01) hyperstereo depth discrimination performance. The use of a two-factor model improves predictive capability (R2 = 0.73); however, the utility of including recovery range scores depended on viewing conditions. When easy viewing conditions (high contrast stimuli presented near the depth of the display) were used, performance was predicted by stereoacuity and the prediction was not improved using recovery range scores. Under difficult viewing conditions (low contrast stimuli, background clutter, crosstalk, and dipvergence), the prediction of hyperstereo performance was significantly improved by including recovery range scores. These results suggest that a binocular fusion recovery range test should be used in conjunction with a stereoacuity test to predict the performance of operators using hyperstereoscopic displays under the more difficult viewing conditions that can be expected in operational environments. Stereoscopic display design considerations and the importance of computer-based vision testing will be discussed in detail.