One approach to estimating the number of cells with high growth potential in a cancer patient is the assessment of tumor cell colony formation in semisolid medium. A potential indicator of the clinical response to a specific drug is the capacity of the drug to reduce the formation of cell colonies. Often, a Poisson log-linear model provides an adequate representation of the dose-response curve. This model is then summarized by the dose required to reduce the number of colonies to a predetermined percentage of the maximum growth. But more general models are needed to account for the overdispersion and the resistant subpopulations often present in these assays. This article explores alternative methods for selecting the dose levels to obtain precise estimates of the parameters of interest. Optimal dose allocations for a single patient or a group of patients are derived. Methods to incorporate the information from pilot studies are discussed. A study of drug sensitivity with leukemia patients provides the framework and motivation for the problem.