A survey is conducted at w of K selection units or lists, e.g. health care institutions or weeks in a year, to estimate N, the total number of individuals with particular characteristics. Our estimator utilizes two items determined for each survey participant: the number, u, among the w lists in S and the number, j, among all K lists on which each survey participant appears. In its traditional form, selection units are chosen using probability sampling and the statistical properties of the estimator derive from the sampling mechanism. Here, selection units are purposively chosen to maximize the chance that they are 'typical' and a model-based analysis is used for inference. If the sample is typical, the ML estimators of N and E(J) are unbiased. If a condition on the second moment of U/J is satisfied, the model-based variance of the estimator of N based on a purposively chosen typical sample is smaller than one based on a randomly chosen sample. Methods to test whether the typical assumption is valid using data from the survey are not yet available. The importance of proper selection of the sample to maximize the chance that it is typical and model breakdown does not occur must be emphasized.