The choice of an appropriate problem-solving method, from available methods, is a crucial skill for experts in many areas. We describe a technique for the automatic selection among methods, which is based on a statistical analysis of their past performances. We formalize the statistical problem involved in selecting an efficient problem-solving method, derive a solution to this problem, and describe a method-selection algorithm. The algorithm not only chooses among available methods, but also decides when to abandon the chosen method, if it proves to take too much time. We give empirical results on the use of this technique in selecting among search engines in the Prodigy planning system.