We investigate whether the classic Mundell-Flemming "trilemma" has morphed into a "dilemma" due to financial globalisation. According to the dilemma hypothesis, global financial cycles determine domestic financial conditions regardless of an economy's exchange rate regime and monetary policy autonomy is possible only if capital mobility is restricted. We find that global financial cycles indeed reduce domestic monetary policy effectiveness in more financially integrated economies. However, we also find that another salient feature of financial globalisation has the opposite effect and amplifies monetary policy effectiveness. Economies increasingly net long in foreign currency experience larger valuation effects on their external balance sheets in response to exchange rate movements triggered by monetary policy impluses. Overall, we find that the net effect of financial globalisation since the 1990s has been to amplify monetary policy effectiveness in the typical advanced and emerging market economy. Specifically, our results suggest that the output effect of a tightening in monetary policy has been stronger by 40% due to financial globalisation. Insofar as valuation effects can only play out if an economy's exchange rate is flexible, the choice of the exchange rate regime remains critical for monetary policy autonomy under capital mobility and in the presence of global financial cycles. Thus, our results suggest that the classic trilemma remains valid.