In this paper we combine the goal directed search of A* with the ability of BDDs to traverse an exponential number of states in polynomial time. We introduce a new algorithm, SetA*, that generalizes A* to expand sets of states in each iteration. SetA* has substantial advantages over BDDA*, the only previous BDD-based A* implementation we are aware of. Our experimental evaluation proves SetA* to be a powerful search paradigm. For some of the studied problems it outperforms BDDA*, A*, and BDD-based breadth-first search by several orders of magnitude. We believe exploring sets of states to be essential when the heuristic function is weak. For problems with strong heuristics, SetA* efficiently specializes to single-state search and consequently challenges single-state heuristic search in general.