This paper develops optimal designs when it is not feasible for every cluster to be representedin a sample as in stratified design, by assuming equal probability two-stage sampling whereclusters are small areas. The paper develops allocation methods for two-stage sample surveyswhere small-area estimates are a priority. We seek efficient allocations where the aim isto minimize the linear combination of the mean squared errors of composite small areaestimators and of an estimator of the overall mean. We suggest some alternative allocationswith a view to minimizing the same objective. Several alternatives, including the area-onlystratified design, are found to perform nearly as well as the optimal allocation but with betterpractical properties. Designs are evaluated numerically using Switzerland canton data aswell as Botswana administrative districts data.

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