Estimation of the ratio of variance components is considered for a balanced one-way random effects model. Problem arises as the readily available estimates can take negative values. Although there are some nonnegative estimates, they do not have any optimum property. Two different paths are followed to cope with this problem. In one way, a class of nonnegative estimates with improved MSE is considered by looking into the structure of the available estimates. In this context, a class of admissible nonnegative estimates is also characterized. In the other a class of nonanalytic estimates (truncated at zero) is formed. © 1992.