Most of human performance is subject to speed–accuracy trade-offs. For spatially constrained aiming, the trade-off is often said to take the specific form of Fitts’ law, in which movement duration is predicted from a single factor combining target distance and target size. However, efforts to extend this law to the three-dimensional context of reaching to grasp (prehension) have had limited success. We suggest that there are potentially confounding influences in standard grasping, and we introduce a novel task to regularize the direction of approach and to eliminate the influences of nearby surfaces. In six participants, we examined speed–accuracy trade-offs for prehension, manipulating the depth (in the plane of the reach), height (orthogonal to the reach), and width (the grasped dimension) of the target object independently. We obtained lawful relationships that were consistent at the group and individual levels. It took longer to reach for more distant objects, and more time was allowed when placing the fingers on a contact surface smaller in either depth or height. More time was taken to grasp wider objects, but only beyond a critical width that varied between individuals. These speed–accuracy trade-offs showed substantial departures from Fitts’ law, and were well described by a two-factor model in which reach distance and object size have separate influences on movement duration. We discuss empirical and theoretical reasons for preferring a two-factor model, and we propose that this may represent the most general form of speed–accuracy trade-off, not only for grasping but also for other spatially constrained aiming tasks.