When faced with medical decisions involving uncertain outcomes, the principles of decision theory hold that we should select the option with the highest expected utility to maximize health over time. Whether a decision proves right or wrong can be learned only in retrospect, when it may become apparent that another course of action would have been preferable. This realization may bring a sense of loss, or regret. When anticipated regret is compelling, a decision maker may choose to violate expected utility theory to avoid regret. We formulate a concept of acceptable regret in medical decision making that explicitly introduces the patient's attitude toward loss of health due to a mistaken decision into decision making. In most cases, minimizing expected regret results in the same decision as maximizing expected utility. However, when acceptable regret is taken into consideration, the threshold probability below which we can comfortably withhold treatment is a function only of the net benefit of the treatment, and the threshold probability above which we can comfortably administer the treatment depends only on the magnitude of the risks associated with the therapy. By considering acceptable regret, we develop new conceptual relations that can help decide whether treatment should be withheld or administered, especially when the diagnosis is uncertain. This may be particularly beneficial in deciding what constitutes futile medical care.