In this paper, the estimators , ASR (P.S.R.S. Rao and Chaubey (1978)), CMINQUE (Chaubey (1983)) and some other modifications of MINQUE similar to that of J.N.K. Rao and Subrahmaniam (1971) are considered for two models (i) The common mean model with heteroscedastic variances and (ii) One way random effects model. These estimators are compared respect to their biases and efficiencies through a Monte Carlo Study. For model (i) weighted means based on different estimators of variances are also compared.