Sensory systems are faced with an essentially infinite number of possible environmental events but have limited processing resources. Posed with this challenge, it makes sense to allocate these resources to prioritize the discrimination of events with the most behavioral relevance. Here, we asked if such relevance is reflected in the processing and perception of motion. We compared human performance on a rapid motion direction discrimination task, including monocular and binocular viewing. In particular, we determined sensitivity and bias for a binocular motion-in-depth (three-dimensional; 3D) stimulus and for its constituent monocular (two-dimensional; 2D) signals over a broad range of speeds. Consistent with prior work, we found that binocular 3D sensitivity was lower than monocular sensitivity for all speeds. Although overall sensitivity was worse for 3D discrimination, we found that the transformation from 2D to 3D motion processing also incorporated a pattern of potentially advantageous biases. One such bias is reflected by a criterion shift that occurs at the level of 3D motion processing and results in an increased hit rate for motion toward the head. We also observed an increase in sensitivity for 3D motion trajectories presented on crossed rather than uncrossed disparity pedestals, privileging motion trajectories closer to the observer. We used these measurements to determine the range of real-world trajectories for which rapid 3D motion discrimination is most useful. These results suggest that the neural mechanisms that underlie motion perception privilege behaviorally relevant motion and provide insights into the nature of human motion sensitivity in the real world.