Economic research in recent years has given considerable prominence to the issue of whether a floating exchange rate provides autonomy with regard to monetary policy to a central bank whose economy is highly open. In particular, Rey (2016) has argued that inflation-targeting advanced economies lack monetary policy autonomy by pointing to results suggesting that U.S. monetary policy shocks matter for the behavior of key financial variables in these economies. In contrast, it is argued in this paper that monetary autonomy does prevail in inflation-targeting advanced economies, notwithstanding the reaction of these economies’ asset prices to U.S. monetary policy developments. The reason is that the monetary-autonomy argument, as advanced by Milton Friedman and as embedded in new open-economy models, rests on the fact that the monetary base is insulated from foreign influences under floating rates. This fact allows the home monetary authority to pursue a stabilization policy in which it has a decisive influence on nominal variables in the long run, as well as a short-run influence on real variables. The result that rest-of-world monetary policy is among the other factors affecting the short-run behavior of real variables (including real asset prices) in a small, floating-rate open economy turns out to be consistent with the traditional and appropriate concept of monetary policy autonomy under floating exchange rates. It follows that such effects of rest-of-world monetary policy on the home economy are consistent with the celebrated open-economy trilemma.