We investigate optimal horizons for targeting inflation in response to different shocks and their properties under alternative preferences of an inflation-targeting central bank. Our analysis is based on a well specified macroeconometric model of Norway, but we examine how alternative specifications of its key equations would affect our results. We find that the optimal horizon is highly shock-specific, precluding general conclusions for demand and supply shocks. An extension of the horizon with concern for output and/or interest rate fluctuations beyond some shock-specific level proves counterproductive. The size of a given shock does not affect the horizon unless the central bank cares about interest rate volatility, while its sign does not matter unless the model is non-linear. The optimal horizon in response to a combination of shocks cannot be derived from those for each of the shocks, as different shocks may amplify or modify the effects of each other. In this case, however, sources of shocks as well as their sizes and signs become relevant, leading to complex dynamics of inflation and output. Successful inflation targeting in such cases may require a complex interest rate response. The optimal horizon generally increases with the degree of persistence in a shock and decreases with the strength of stabilisation mechanisms in the model.