Most analyses of monetary policy delegation schemes typically ignore the behavior of the fiscal policy maker. The paper investigates how monetary price level targeting or monetary nominal income targeting may yield social gain in an economy with government debt and where the fiscal policymaker, acting strategically, may take counter actions. We argue that the choice of fiscal policy instrument plays an important role for the performance of monetary policy. The optimal choice of monetary policy delegation scheme depends crucially on the level of government debt and its maturity, with a switch from price level targeting being desirable to nominal income targets being strongly preferred as debt levels rise and maturity shortens.