Inflation target regimes with both explicit inflation and implicit employment goals can be improved by a 'conservative' central bank. This type of bank can eliminate inflation bias and mimic an optimal inflation contract, outperforming other types of central banks. However, when employment persistence is considered, a state-contingent inflation bias and stabilization bias may arise. Despite this, a constant inflation target and a constant inflation contract remain equivalent. By combining a state-contingent inflation target with a weight-conservative central bank, the equilibrium corresponding to an optimal rule under commitment can be achieved.