It is well known that the performance of a stochastic local search procedure depends upon the setting of its noise parameter, and that the optimal setting varies with the problem distribution. It is therefore desirable to develop general priniciples for tuning the procedures. We present two statistical measures of the local search process that allow one to quickly find the optimal noise settings. These properties are independent of the fine details of the local search strategies, and appear to be relatively independent of the structure of the problem domains. We applied these principles to the problem of evaluating new search heuristics, and discovered two promising new strategies.