Rotating 3D objects is a difficult task. We present a new rotation technique based on collision-free “mating” to expedite 3D rotations. It is specifically designed for one-handed interaction on tablets or touchscreens. A user study found that our new technique decreased the time to rotate objects in 3D by more than 60% in situations where objects align. We found similar results when users translated and rotated objects in a 3D scene. Also, angle errors were 35% less with mating. In essence, our new rotation technique improves both the speed and accuracy of common 3D rotation tasks.