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.