A heuristic criterion for choosing an acceptable level of bias in ridge regression is presented. The criterion is based on a noncentral F-test of the stochastic restrictions implicit in the ridge estimator. An appropriate significance level for the test is based on conjunctive use of strong and weak mean square error criteria. The procedure is illustrated in estimating a Cobb-Douglas production function for the Central Valley of California using factor shares as priors rather than the null vector. Preliminary results suggest that a conjunctive SMSE/WMSE criterion with more "reasonable" priors selects an estimator with smaller bias than ridge trace.