Abstract There are many hard shortest-path search problems that cannot be solved, because best-first search runs out of memory space and depth-first search runs out of time. We propose Forward Perimeter Search (FPS), a heuristic search with controlled use of memory. It builds a perimeter around the root node and tests each perimeter node for a shortest path to the goal. The perimeter is adaptively extended towards the goal during the search process. We show that FPS expands in random 24-puzzles 50% fewer nodes than BF-IDA* while requiring several orders of magnitude less memory. Additionally, we present a hard problem instance of the 24-puzzle that needs at least 140 moves to solve; i.e. 26 more moves than the previously published hardest instance.