Many distributional conflicts are characterized by the presence of acquired rights. The basic structure of these conflicts is that of the so-called claims problem, in which an amount of money has to be divided among individuals with differing claims and the total amount available falls short of the sum of the claims. We describe the results of a questionnaire in which Belgian and German students were confronted with nine claims problems. In the “Firm” version, respondents had to divide revenue among the owners of a firm who contribute to the activities of the firm in different degrees. In the “Pensions” version, they had to divide tax money among pensioners who have paid different contributions during their active career. Responses in the Pensions version are more egalitarian than in the Firm version. For both versions, the proportional rule performs very well in describing the choices of the respondents. Other prominent rules—in particular the constrained equal awards and constrained equal losses rules— fail to capture some basic intuitions. A substantial part of the respondents tend to become more progressive as the amount to be distributed decreases other things equal, and tend to become more progressive as the inequality in the distribution of claims becomes more unequal other things equal. All of these conclusions are robust with respect to the difference in home-country of the respondents.