A 1990s view is that inflation is best avoided by delegating monetary policy to an independent central bank. However most analyses overlook fiscal policy, which cannot be delegated. Here we make a very simple extension of the usual policy game by introducing the government as a third player, in charge of a fiscal instrument for demand management. If the government delegates monetary policy, there will be a battle over aggregate demand. Although the bank wins, so that inflation is avoided, it is as the cost of an excessive interest rate. Society's welfare may be lower than with no delegation.