We provide a method, based on the theory of Markov decision problems, for e cient planning in stochastic domains. Goals are encoded as reward functions, expressing the desirability of each world state; the planner must nd a policy (mapping from states to actions) that maximizes future rewards. Standard goals of achievement, as well as goals of maintenance and prioritized combinations of goals, can be speci ed in this way. An optimal policy can be found using existing methods, but these methods are at best polynomial in the number of states in the domain, where the number of states is exponential in the number of propositions (or state variables). By using information about the starting state, the reward function, and the transition probabilities of the domain, we can restrict the planner's attention to a set of world states that are likely to be encountered in satisfying the goal. Furthermore, the planner can generate more or less complete plans depending on the time it has available. We describe experiments involving a mobile robotics application and consider the problem of scheduling di erent phases of the planning algorithm given time constraints.