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Many search trees are impractically large to explore exhaustively. Recently, techniques like limited discrepancy search have been proposed for improving the chance of nding a goal in a limited amount of search. Depth-bounded discrepancy search o ers such a hope. The motivation behind depth-bounded discrepancy search is that branching heuristics are more likely to be wrong at the top of the tree than at the bottom. We therefore combine one of the best features of limited discrepancy search {the ability to undo early mistakes {with the completeness of iterative deepening search. We show theoretically and experimentally that this novel combination outperforms existing techniques.