The Programme for Government indicated that under a Universal Health Insurance system, the State would "pay insurance premia for people on low incomes and subsidise premia for people on middle incomes". This paper examines issues in the design of such a subsidy scheme, in the context of overall premium costs as estimated by Wren et al. (2015) and the KPMG (2015) study for the Health Insurance Authority. Subsidy design could involve a step-level system, similar to the medical card and GP visit card in the current system; or a smooth, tapered withdrawal of the subsidy, similar to what obtains for many cash benefits in the welfare system. The trade-offs between the income limit up to which a full subsidy would be payable, the rate of withdrawal of subsidy with respect to extra income and overall subsidy cost are explored.