This paper uses a small, calibrated forward-looking model of the euro-area economy to investigate the implications of incomplete information about potential output for the conduct and the design of monetary policy. Three sets of issues are examined. First, the certainty-equivalent optimal policy under both commitment and discretion is characterised. In both cases, incomplete information about potential output leads to very persistent deviations between the actual and the perceived output gap in response to supply and cost-push shocks. The costs of imperfect information are quite large. Second, the implications for simple policy rules such as Taylor or inflation-forecast rule are examined. In first-difference form, both rules continue to perform relatively well with imperfect information as long as the output gap and the inflation forecast are optimally estimated. Third, the implications of potential output uncertainty for the optimal delegation to an independent central bank are examined. Incomplete information implies that it is optimal to appoint a more 'hawkish' central bank.