In this report, selection theory is used as a theoretical framework from which mathematical algorithms for tailored testing are derived. The process of tailored, or adaptive, testing is presented as analogous to personnel selection and rejection on a series of continuous variables that are related to ability. Proceeding from a single common-factor model, the author derives the two- and three-parameter normal ogive item response functions as submodels. For both of these submodels, algorithms are developed for sequential item selection, ability estimation, and test termination in the context of adaptive ability testing. It is shown that the adaptive testing method based on these algorithms is formally identical to a previously developed Bayesian sequential tailored testing procedure. (Author)