The ability to quickly compute shortest paths in 3D grids is a technological enabler for several applications such as pipe routing and computer video games. The main challenge is how to deal with the many symmetric permutations of each shortest path. We tackle this problem by adapting Jump Point Search (JPS), a well-known symmetry breaking technique developed for fast pathfinding in 2D grids. We give a rigorous reformulation of the JPS pathfinding system into 3D and we prove that our new algorithm, JPS-3D, is optimality preserving. We also develop a novel method for limiting scan depth during jump operations, which can further reduce search time. Experimental results show significant improvements versus online A* search and previous attempts at generalising JPS. We demonstrate that searching with adaptive scan limits can yield additional speedups of over an order of magnitude.