In the presence of multicollinearity ridge regression techniques result in estimated coefficients that are biased but have a smaller variance than ordinary least squares (OLS) estimators and may, therefore, have a smaller mean square error. The directed ridge estimator (DRE) suggested here alters only diagonal elements corresponding to relatively small eigenvalues. The advantage of our method is that the resulting estimates may be less biased than in other ridge regression methods that alter all diagonal elements. A set of experiments indicate that various ridge estimators result in reduced mean square error in the coefficient estimates relative to OLS and that DRE performs well relative to the others.