It has recently been shown that local search is surprisingly good at nding satisfying assignments for certain classes of CNF formulas (Sel-man et al. 1992). In this paper we demonstrate that the power of local search for satissability testing can be further enhanced by employing a new strategy, called \mixed random walk", for escaping from local minima. We present a detailed comparison of this strategy with simulated annealing, and show that mixed random walk is the superior strategy on several classes of computationally diicult problem instances. We also present results demonstrating the eeectiveness of local search with walk for solving circuit synthesis and diagnosis problems. Finally, we show that mixed random walk improves upon the results of Hansen and Jaumard on MAX-SAT problems.