Population structure is a key determinant of the efficiency of sampling plans and estimators. Variables in many establishment populations have structures that can be described by simple linear models with a single auxiliary variable and a variance related to some power of that auxiliary. If a working model can be devised that is a good approximation to the population structure, then very efficient sample designs and estimators are possible. This study compares alternative strategies of (i) selecting a pilot study to estimate the variance power and using that estimate to select a main sample and (ii) selecting a only main sample based on an educated guess about the variance power. We also examine a number of sampling plans, including probability proportional to size, deep stratification based on a measure of size, and weighted balanced sampling. Population totals are estimated by best linear unbiased predictors, general regression estimators, and some other choices often used in practice. – See more at: https://ojs.ub.uni-konstanz.de/srm/article/view/72#sthash.6vNptnHy.dpuf