Abstract Bounded suboptimal search algorithms offer shorter solving times by sacri?cing optimality and instead guaranteeing solution costs within a desired factor of optimal. Typically these algorithms use a single admissible heuristic both for guiding search and bounding solution cost. In this paper, we present a new approach to bounded suboptimal search, Explicit Estimation Search, that separates these roles, consulting potentially inadmissible information to determine search order and using admissible information to guarantee the cost bound. Unlike previous proposals, it successfully combines estimates of solution length and solution cost to predict which node will lead most quickly to a solution within the suboptimality bound. An empirical evaluation across six diverse benchmark domains shows that Explicit Estimation Search is competitive with the previous state of the art in domains with unit-cost actions and substantially outperforms previously proposed techniques for domains in which solution cost and length can differ.