This note proposes a new set-up for the fund backing the Single Resolution Mechanism (SRM). The proposed fund is a Multi-Tier Resolution Fund (MTRF), restricting the joint and several supranational liability to a limited range of losses, bounded by national liability at the upper and the lower end. The layers are, in ascending order: a national fund (first losses), a European fund (second losses), the national budget (third losses), the ESM (fourth losses, as a backup for sovereigns). The system works like a reinsurance scheme, providing clear limits to European-level joint liability, and therefore confining moral hazard. At the same time, it allows for some degree of risk sharing, which is important for financial stability if shocks to the financial system are exogenous (e.g., of a supranational macroeconomic nature). The text has four parts. Section A describes the operation of the Multi-Tier Resolution Fund, assuming the fund capital to be fully paid-in (Steady State). Section B deals with the build-up phase of the fund capital (Build up). Section C discusses how the proposal deals with the apparent incentive conflicts. The final Section D summarizes open questions which need further thought (Open Questions).