The veil of ignorance has been used often as a tool for recommending what justice requires with respect to the distribution of wealth. We complete Harsanyi's model of the veil of ignorance by appending information permitting objective comparisons among persons. In order to do so, we introduce the concept of objective empathy. We show that the veil-of-ignorance conception of John Harsanyi, so completed, and Ronald Dworkin's, when modelled formally, recommend wealth allocations in conflict with the prominently espoused view that priority should be given to the less able in wealth allocation. We finally argue that the veil of ignorance should be rejected as a tool for discovering what justice requires