The problem of simultaneous estimation of variance components is considered for a balanced hierarchical mixed model under a sum of squared error loss. A new class of estimators is suggested which dominate the usual sensible estimators. These estimators shrink towards the geometric mean of the component mean squares that appear in the ANOVA table. Numerical results are tabled to exhibit the improvement in risk under a simple model. © 1991, Taylor & Francis Group, LLC. All rights reserved.