The authors provide a new model within the framework of theories of bounded rationality for the observed physicians' behavior that their ordering of diagnostic tests may not be rational. Contrary to the prevailing thinking, the authors find that physicians do not act irrationally or inappropriately when they order diagnostic tests in usual clinical practice. When acceptable regret (i.e., regret that a decision maker finds tolerable upon making a wrong decision) is taken into account, the authors show that physicians tend to order diagnostic tests at a higher level of pretest probability of disease than predicted by expected utility theory. They also show why physicians tend to overtest when regret about erroneous decisions is extremely small. Finally, they explain variations in the practice of medicine. They demonstrate that in the same clinical situation, different decision makers might have different acceptable regret thresholds for withholding treatment, for ordering a diagnostic test, or for administering treatment. This in turn means that for some decision makers, the most rational strategy is to do nothing, whereas for others, it may be to order a diagnostic test, and still for others, choosing treatment may be the most rational course of action.