The objective of this paper is to investigate the "conventional wisdom" that there is a policy conflict between the reduction of inequality and the encouragement of entrepreneurial risk taking. The paper attempts to provide a precise statement of this conflict in the context of the progressivity of tax regimes. Using the method of inequality decomposition analysis, a taxonomy is developed which locates the sources of the policy conflict in a precise fashion. A detailed analysis then shows that the conventional wisdom is misleading if not wrong, and that in many cases the claimed policy conflict is quite simply illusory.