Inflation targeting countries generally define the inflation objective in terms of the consumer price index. Studies in the academic literature, however, reach conflicting conclusions concerning which measure of inflation a central bank should target in a small open economy. This paper examines the properties of domestic, CPI, and real-exchange- rate-adjusted (REX) inflation targeting. In one class of open economy New Keynesian models there is an isomorphism between optimal policy in an open versus closed economy. In the type of model we consider, where the real exchange rate appears in the Phillips curve, this isomorphism breaks down; openness matters. REX inflation targeting restores the isomorphism but this may not be desirable. Instead, under domestic and CPI inflation targeting the exchange rate channel can be exploited to enhance the effects of monetary policy. Our results indicate that CPI inflation targeting delivers price stability across the three inflation objectives and will be desirable to a central bank with a high aversion to inflation instability. CPI inflation targeting also does a better job of stabilizing the real exchange rate and interest rate which is an advantage from the standpoint of financial stability. REX inflation targeting does well in achieving output stability and has an advantage if demand shocks are predominant. In general, the choice of the inflation objective affects the trade-offs between policy goals and thus policy choices and outcomes.