Limited resources are the permanent condition in health care. Rationing, according to H. Kliemt, is the distribution of limited resources below market prices to all people in need for these resources. Therefore, rationing is a basic component of every kind of human health care system. However, the crucial problem is how to find just and fair rules ... for this distribution under the premise, that every patient should have the same chance. The allocation of organs for transplant can serve as a paradigmatic example for studying rationing problems, as shortage of organs cannot be denied nor abolished. H. Kliemt compared the situation with the classic decathlon. The selection of factors and the combination and weighing of these factors for `winning a donor organ' should strictly be related to individuals. Non-medical criteria should generally be accepted and authorized as far as they are relevant to the question of justice and fairness. In this paper the so-called `solidarity model', an example of joint research with Hartmut Kliemt, is introduced as an allocation system with the power to enhance justice and fairness.