Many regression programs include a tolerance test that does not allow a variable to enter the regression if its correlation with the previously entered variables exceeds a specified level. This is done to achieve computational stability by assuring that the correlation matrixCof the independent variables is not nearly singular. However, for any specified tolerance level, there is an example in which the entering variables pass the tolerance test but the computation is extremely unstable. A bound for the condition ofCisptimes the trace ofC-1, which can be monitored instead of tolerance to assure stability.