A new solution is presented to the problem of controlling the motion of a crane’s suspended load through arbitrarily complex, 3D paths through the crane’s manoeuvre space. A generalized boom crane arrangement is considered, so that gantry and luffing arrangements are included as particular cases. Thus the crane’s boom slews about a central, vertical (tower) axis. This boom is either a horizontal gantry with a trolley moving radially along it, from which the load can be winched, or a jib, which can rotate in the vertical plane, with the hoisting cable passing over a pulley attached at its end point. In either case, there are three directly controlled motion variables, the effects of which on the suspended payload’s motion are strongly cross-coupled. The challenge is to enable the payload to follow the desired 3D path as closely as possible during the manoeuvre, and come to rest rapidly at target, by directly controlling these three actuating motions. Thus the controller must achieve position control combined with active swing suppression throughout the manoeuvre and on arrival at the desired end point. A model is developed of the generalized crane for both gantry and luffing crane types. The proposed control strategy is then applied and tested on this model. The controller is based on mechanical wave concepts. When applied to the model, it is shown to be very effective. It is accurate, robust to system changes and actuator limitations, very stable, requires sensing only at the trolley (and not at payload), and is easy to implement.