This paper examines the moral and professional issues present in cases involving continued treatment of fatally ill patients in order to benefit a third party. It is argued that such treatment can be justified in some cases from a moral point of view. Practical considerations make such cases difficult to identify at times. It is also argued on the other hand that professional concerns should rule out the permissibility of continuing such treatment. Thus, even though it may be morally permissible at times to continue treatment, it is not good medical practice to do so.