In real world planning problems, time for deliberation is often limited. Anytime planners are well suited for these problems: they find a feasible solution quickly and then continually work on improving it until time runs out. In this paper we propose an anytime heuristic search, ARA*, which tunes its performance bound based on available search time. It starts by finding a suboptimal solution quickly using a loose bound, then tightens the bound progressively as time allows. Given enough time it finds a provably optimal solution. While improving its bound, ARA* reuses previous search efforts and, as a result, is significantly more efficient than other anytime search methods. In addition to our theoretical analysis, we demonstrate the practical utility of ARA* with experiments on a simulated robot kinematic arm and a dynamic path planning problem for an outdoor rover.