One of the problems inherent in variance component estimation centers around inadmissible estimates. Such estimates occur when there is more variability within groups, relative to between groups. This paper suggests a Bayesian approach to resolve inadmissibility by placing noninformative inverse-gamma priors on the variance components, and compares Bayesian estimates with expected mean square and maximum likelihood estimates. No noticeable differences among estimation type were found for balanced data. However, Bayesian estimates tended to produce less biased estimates for unbalanced data. (Contains 12 figures and 7 tables.)