Patients who are seriously ill may ask doctors to treat them with unapproved medication, about which not much is known, or else with known medication in a high dosage. Apart from strict legal constraints such cases may involve difficult ethical questions as e.g. how long a series of treatments of different patients should be continued. Similar questions also arise in less serious situations. A physician trusts that a certain combination of freely available drugs are efficient against a specific disease and tries to help patients and to follow at the same time the primum-non-nocere principle. The objective of this paper is to contribute to the research on such questions in the form of mathematical models. Arguing in a step-to-step approach, we will show that certain sequential optimisation problems comply in a natural way with the true spirit of major ethical principles in medicine. We then suggest protocols and associate algorithms to find optimal, or approximately optimal, treatment strategies. Although the contribution may sometimes be difficult to apply in medical practice, the author thinks that the rational behind the approach offers a valuable alternative for finding decision support and should attract attention.