Estimation problem in presence of uncertain prior information about the mean of the location-scale model for some t-populations is investigated. The Student-t distribution, a typical member of the elliptical family of distributions, encompasses the normal as well as the Cauchy distributions in the two extremes. Univariate model is considered for both one-sample and two-sample cases with unknown but equal population variance(s). In each case, the unrestricted, restricted and preliminary test maximum likelihood estimators are defined. The expressions for the bias and the mean square error of the three estimators are provided and the relative efficiencies are analysed. A maximin criterion is established and graphs and tables are constructed for different number of degrees of freedom (D.F.) as well as sample sizes. These tables of relative efficiencies can be used to determine a proper choice of the significance level of the preliminary test which in turn determines the choice of the estimator.