Koop  proved that interpenetrating samples of unequal sizes are more efficient than those with equal sizes for estimating a finite population total. After observing that there is a serious lacuna present in his proof, a correct proof has been suggested. The optimum choice of individual sample sizes has also been discussed for a given (i) total sample size, (ii) cost and (iii) precision, with an assumed cost structure. Finally, the resulting estimators have been compared with those based on a single sample. © 1982 Physica-Verlag.