One of the underlying ethical values of the Patient Self-Determination Act (PSDA) is the legal right of patients to decide on their own medical care, i.e., to accept or refuse medical treatment. Yet, there is a growing concern that a patient's legal right to determine medical treatment might result in health care professionals violating their own personal and/or professional ethical values. I shall therefore briefly review the requirements of the PSDA and outline the consequences of this act for a particular case. The application of the Act becomes problematic in this case because the health care professionals involved believe that the treatments involved are medically futile. I consider the potential conflict between autonomy and futility. The thesis defended is that patient autonomy is not an absolute moral right and that health care professionals are not only permitted, but are sometimes morally required, to withhold and/or withdraw futile treatments even if the patient or the patient's surrogate request (demand!) that the treatments be continued.