Three sampling designs are considered for estimating the sum ofkpopulation means by the sum of the corresponding sample means. These are (a) the optimal design; (b) equal sample sizes from all populations; and (c) sample sizes that render equal variances to all sample means. Designs (b) and (c) are equally inefficient, and may yield a variance up toktimes as large as that of (a). Similar results are true when the cost of sampling is introduced, and they depend on the population sampled.