A central bank pursuing the policy of inflation targeting aims to keep inflation as close as possible to a pre-announced value. But which 'inflation' should this be? Quarterly, annual, biennial? In theoretical models it is typically inflation during one period. We analyze how changing the period over which the inflation rate is defined - i.e. changing central bank preferences - affects optimal monetary policy. It is shown that when targeting inflation is the sole objective of the central bank, more aggressive monetary policy results; but when output stabilization is also a concern, a 'longer-term view' typically leads to a more cautious conduct of monetary policy and less variability in output. The conditions under which inflation targeting in effect becomes price level targeting are also examined.