The Markowitz mean-variance framework is the foundation of modern portfolio theory. One problem with this approach, however, is how sample covariance matrices tend to underestimate risk. Since the biases of optimized portfolios are closely related to eigenfactor portfolios, we present a methodology for estimating biases in eigenfactor volatilities, and for adjusting the covariance matrix to remove such biases. By removing the biases of the eigenfactors, we remove the biases of optimized portfolios. We also find that eigen-adjusted covariance matrices reduce the out-of-sample volatilities of optimized portfolios.