Iterative Bounding LAO* is a new algorithm for epsilon- optimal probabilistic planning problems where an absorbing goal state should be reached at a minimum expected cost from a given initial state. The algorithm is based on the LAO* algorithm for finding optimal solutions in cyclic AND/OR graphs. The new algorithm uses two heuristics, one upper bound and one lower bound of the optimal cost. The search is guided by the lower bound as in LAO*, while the upper bound is used to prune search branches. The algorithm has a new mechanism for expanding search nodes, and while maintaining the error bounds, it may use weighted heuristics to reduce the size of the explored search space. In empirical tests on benchmark problems, Iterative Bounding LAO* expands fewer search nodes compared to state of the art RTDP variants that also use two-sided bounds.