We report results from a formal user study of interactive 3D rotation using the mouse-driven Virtual Sphere and Arcball techniques, as well as multidimensional input techniques based on magnetic orientation sensors. Multidimensional input is often assumed to allow users to work quickly, but at the cost of precision, due to the instability of the hand moving in the open air. We show that, at least for the orientation matching task used in this experiment, users can take advantage of the integrated degrees of freedom provided by multidimensional input without necessarily sacrificing precision: using multidimensional input, users completed the experimental task up to 36% faster without any statistically detectable loss of accuracy. We also report detailed observations of common usability problems when first encountering the techniques. Our observations suggest some design issues for 3D input devices. For example, the physical form-factors of the 3D input device significantly influenced user acceptance of otherwise identical input sensors. The device should afford some tactile cues, so the user can feel its orientation without looking at it. In the absence of such cues, some test users were unsure of how to use the device.