Is a debt-concerned monetary authority desirable? This article deals with the impact of fiscal-monetary policy interactions in a monetary union on countryspecific and union-wide debt stabilization, when the authorities act strategically. The focus is on the impact that monetary policy would have on a debt-concerned fiscal authority through the debt constraint and the corresponding interaction with decentralized fiscal policies. It is shown that the fiscal-monetary (overall) policy coordination strategic regime delivers better results than the non-cooperative regime for both the output gap and the outstanding level of debt at the union level. Two further institutional arrangements are investigated and compared: An authority-based preventive procedure, which works through a debt-concerned monetary authority, and a market-based one, which works through financial markets by assuming a risk premium on country-specific nominal interest rates according to the countryspecific fiscal stances. The risk premium acts as a form of 'market-based' discipline. Both regimes stand between the decentralized and the centralized setting. The central bank's optimal weight on union-wide debt stabilization is computed when financial markets provide discipline to the fiscal authorities. It is optimal for the social planner to appoint a debt-concerned central banker, if there is a degree of conservatism from the monetary authority, and/or if the social planner cares about union-wide debt stabilization. A higher risk premium parameter enhances the impact of the former on the optimal weight on union-wide debt stabilization, while it reduces the impact of the latter.