Navigational path planning is a classical problem in robotics. Traditional approaches use goal-directed heuristic search of problem spaces defined by spatial models of the navigation world. Case-based reasoning offers an alternative approach. In the Router project, we have combined the case-based method with the model-based method. Since Router is a multistrategy system, it provides an experimental testbed to study some of the hypotheses of case-based reasoning. In this paper, we report on a set of experiments that examine four hypotheses: (i) the case-based method more efficient than the model-based method, (il) the case-based method produces plans of quality equal to those produced by the model-based method, (iii) the case-based method requires less knowledge but has the same problem-solving coverage as the model-based method, and (iv) cases need to be decomposed into partial cases for efficient and effective problem solving. We find that while hypothesis (i) is true, the others are questionable.