Diagnostic testing confronts several challenges at once, among which are issues of test interpretation and immediate modification of the test itself in response to the interpretation. Several methods are available for administering and evaluating a test in real-time, towards optimizing the examiner's chances of isolating a persistent pattern of erroneous performance by a student. Under ideal circumstances, a student who misunderstands the test content would be identified early in a testing sequence; from this point the test could be tailored to estimates not only of ability but also (or instead) to the relative likelihoods of a set of competing diagnostic hypotheses that could account for the student's behavior (ability). Items which could discriminate among these hypotheses could be administered in increasingly well-bounded subsets until a specified stopping rule is met. The following models for this procedure are described and compared: Wald's sequential probability ratio test, Sixtl's modified binomial method, Choppin's catenating Bayesian method, Fink and Galen's decision path method, Shortliffe and Buchanan's inexact reasoning method, Kmietowicz and Pearson's ranked probability method, and Schum's cascaded inference method. (BW)