Do arm postures vary with the speed of reaching? For reaching movements in one plane, the hand has been observed to follow a similar path regardless of speed. Recent work on the control of more complex reaching movements raises the question of whether a similar "speed invariance" also holds for the additional degrees of freedom. Therefore we examined human arm movements involving initial and final hand locations distributed throughout the three-dimensional (3D) workspace of the arm. Despite this added complexity, arm kinematics (summarized by the spatial orientation of the "plane of the arm" and the 3D curvature of the hand path) changed very little for movements performed over a wide range of speeds. If the total force (dynamic + quasistatic) had been optimized by the control system (e.g., as in a minimization of the change in joint torques or the change in muscular forces), the optimal solution would change with speed; slow movements would reflect the minimal antigravity torques, whereas fast movements would be more strongly influenced by dynamic factors. The speed-invariant postures observed in this study are instead consistent with a hypothesized optimization of only the dynamic forces.