Three stage sampling procedures have been discussed with the goal of achieving (i) the minimum risk and (ii) the bounded risk separately for point estimation of the mean of a normal population whose variance is completely unknown. The remainder term in the second-order asymptotic expansion of the risk function is shown to have the exact same order as that obtained in the case of the corresponding purely sequential procedure for both these problems. The results obtained for the second problem also form major extensions of the properties derived in Mukhopadhyay (1985, Sequential Analysis, 4, 311-319)