Abstract: Recently, Schneeberger. H considered allocations of the second-stage sampling units in two stage sampling according to simple random method at both stages. In this paper, we consider allocations of the second-stage sampling units in two-stage sampling according to unequal probability method at first stage and simple random method at second stage. We compare the variations of the estimators for the population total with various allocations of the second-stage sampling units, indicating optimum allocation of the second-stage sampling units and respective gains in precision.