The notion of the veil has been used to argue that higher degrees of uncertainty would make people choose higher degrees of redistribution. We test this hypothesis theoretically and experimentally. In the game, individuals first choose a redistribution rule before they decide upon an investment on the post-constitutional level. We vary the information on the individual productivity of investments and find that the level of redistribution does not decrease with the degree of uncertainty. However, compared with the theoretical benchmark, there is too little redistribution under full uncertainty, and too much under partial uncertainty. For all degrees of uncertainty, we find a coexistence of libertarianism and redistribution as well as incomplete sorting, so that heterogenous redistribution communities turn out to be sustainable.