Formulas describing optimum sample allocation in stratified and two-stage sample designs are given ordinarily in terms of “best” estimates of a population mean or total. The best allocation for estimating the variance of the mean may depart from that which is optimum for the mean. For stratified sampling, such a departure depends upon variation among strata in functions of coefficients of kurtosis for the strata (fourth moment ÷ squared second moment). For two-stage designs optimum sample allocation for estimating the variance of the mean depends upon coefficients of kurtosis as well as costs and variance components. Examination of the expressions for optimum variance estimation and some calculations for specific cases indicate that losses in efficiency of variance estimates due to using optimum allocation for a mean are not extreme in a variety of particular cases.