A framework for decision-making is introduced in which two out of five patients will be denied treatment. Certain resource constraints are accepted in this hypothetical example. The authors' own ranking of five patients from a department of internal medicine are presented. It was not difficult to select the highest prioritized patients. However, ranking of the remaining patients revealed considerable controversy. Emphasis is therefore laid on the reasons given for each ranking. An interesting finding is that variations in awarding priority to some cases are clearly based on disagreement about facts, not values. The article concludes by suggesting a classification of selection criteria for priority setting based on a distinction between necessary, controversial and unacceptable criteria. The article is presented in an attempt to stimulate a debate about priority setting in everyday hospital work.