Progress towards Universal Health Coverage (UHC) requires making difficult trade-offs. In this journal, Dr. Margaret Chan, the WHO Director-General, has endorsed the principles for making such decisions put forward by the WHO Consultative Group on Equity and UHC. These principles include maximizing population health, priority for the worse off, and shielding people from health-related financial risks. But how should one apply these principles in particular cases and how should one adjudicate between them when their demands conflict? This paper by some (...) members of the Consultative Group and a diverse group of health policy professionals addresses these questions. It considers three stylized versions of actual policy dilemmas. Each of these cases pertains to one of the three principal dimensions of progress towards UHC: which services to cover first, which populations to prioritize for coverage, and how to move from out-of-pocket expenditures to pre-payment with pooling of funds. Our cases are simplified to highlight common trade-offs. While we make specific recommendations, our primary aim is to demonstrate both the form and substance of the reasoning involved in striking a fair balance between competing interests on the road to UHC. (shrink)