We present LeviCursor, a method for interactively moving a physical, levitating particle in 3D with high agility. The levitating object can move continuously and smoothly in any direction. We optimize the transducer phases for each possible levitation point independently. Using precomputation, our system can determine the optimal transducer phases within a few microseconds and achieves round-trip latencies of 15 ms. Due to our interpolation scheme, the levitated object can be controlled almost instantaneously with sub-millimeter accuracy. We present a particle stabilization mechanism which ensures the levitating particle is always in the main levitation trap. Lastly, we conduct the first Fitts' law-type pointing study with a real 3D cursor, where participants control the movement of the levitated cursor between two physical targets. The results of the user study demonstrate that using LeviCursor, users reach performance comparable to that of a mouse pointer.