Classical propositional STRIPS planning is nothing but the search for a path in the state transition graph induced by the operators in the planning problem. What makes the problem hard is the size and the sometimes adverse structure of this graph. We conjecture that the search for a plan would be more efficient if there were only a small number of paths from the initial state to the goal state. To verify this conjecture, we define the notion of reduced operator sets and describe ways of finding such reduced sets. We demonstrate that some state-of-the-art planners run faster using reduced operator sets.