For many real-world problems, environments at the time of planning are only partiallyknown. For example, robots often have to navigate partially-known terrains, planes often have to be scheduled under changing weather conditions, and car route-finders often have to figure out paths with only partial knowledge of traffic congestions. While general decisiontheoretic planning that takes into account the uncertainty about the environment is hard to scale to large problems, many such problems exhibit a special property: one can clearly identify beforehand the best (called clearly preferred) values for the variables that represent the unknowns in the environment. For example, in the robot navigation problem, it is always preferred to find out that an initially unknown location is traversable rather than not, in the plane scheduling problem, it is always preferred for the weather to remain a good flying weather, and in route-finding problem, it is always preferred for the road of interest to be clear of traffic. It turns out that the existence of the clear preferences can be used to construct an efficient planner, called PPCP (Probabilistic Planning with Clear Preferences), that solves these planning problems by running a series of deterministic low-dimensional A*-like searches. In this paper, we formally define the notion of clear preferences on missing information, present the PPCP algorithm together with its extensive theoretical analysis, describe several useful extensions and optimizations of the algorithm and demonstrate the usefulness of PPCP on several applications in robotics. The theoretical analysis shows that once converged, the plan returned by PPCP is guaranteed to be optimal under certain conditions. The experimental analysis shows that running a series of fast low-dimensional searches turns out to be much faster than solving the full problem at once since memory requirements are much lower and deterministic searches are orders of magnitude faster than probabilistic planning.