This paper studies central bank independence in a model of a monetary union where fiscal policies remain the responsibility of national governments and generate externalities. Governments may either coordinate fiscal policy or not, and three forms of delegation are considered: Rogoff-type 'weight independence', inflation targets and linear inflation contracts. The key results are as follows. Under fiscal coordination, 'convervatism' holds and targets (or contracts) outperform 'weight independence'. Without fiscal coordination, 'anti-conservatism' may be optimal when fiscal spillovers are negative, as it reduces governments' activism; and 'weight independence' is restored, since it can alleviate distortions in shock stabilization.