This paper studies optimal stabilisation policies under commitment when monetary policy sets nominal interest rates and fiscal policy decides on public expenditure, income tax rates, and issuance of nominal non-contingent debt. High levels of government debt adversely affect the steady state of the economy and increase aggregate volatility. The latter emerges because debt exposes the government budget to real interest rate risk and thereby induces stronger volatility of taxes and public spending. The optimal variability of fiscal deficits is found to increase with the level of government debt, while the optimal variability of nominal interest rates decreases. Overall, optimal stabilisation policy does not require annual fiscal deficits to deviate by more than 3 percentage points of GDP from their steady state value or nominal interest rates to fall all the way to zero. Only if the standard deviation of economic disturbances is two to three times larger than suggested by post-war evidence do such events occur with non-negligible probability.