We present an experiment that sets up a context of production of a common output obtained by using production means that are randomly and unequally distributed. Before the production phase, subjects must choose a distributive principle for the output division, under ignorance of the allocation of the production means. Subsequently, they make a distributive choice fully aware of their luck and performance. The aim of the experiment is to test, first, whether ordinary subjects in an impartial situation are capable of converging on a fair principle of distribution – able of redressing the arbitrariness of the initial production means allocation; and second, whether these same ordinary subjects are capable of actually following that principle in a real distributive choice that excludes coercion, reputation effects and other forms of social pressures. The main finding is that a distributive rule that redresses initial inequalities is both accepted ex-ante and actually applied ex-post by most individuals. Our conclusion is relevant for the issue of realism of normative theories of justice and the possibility of institution design aimed at implementing distributive justice principles and policies.