Abstract Recent research has shown that optimal monetary policy may display considerable price-level drift. Proponents of price-level targeting have argued that the costs of eliminating the price-level drift may be reduced if the central bank responds flexibly by returning the price level only gradually to the target path ( Gaspar et al., 2010 ). We revisit this argument in two variants of the New Keynesian model. We show that in a two-sector version of the model which allows for changes in relative prices across sectors, the costs of stabilisation under price-level targeting remain much higher than under inflation targeting for all policy-relevant horizons. Our conclusion is that extending the policy horizon is not a panacea to reduce the costs of eliminating price-level drift.