With the recent tensions within the euro area, the Swiss franc appreciated sharply against the euro, playing the role of international safe-haven currency. Although Switzerland is not a member of the European Union (EU), its high degree of de facto integration to it make that such appreciation is transmitted to the real economy. Thus, if the independence and autonomy of Switzerland's official currency in Europe has advantages, it also entails significant costs, particularly related to the special status of the Swiss franc. In this article we study the desirability and viability for Switzerland of a ″median″ monetary integration to the EU to help ease the external constraint of the exchange rate, namely a de jure anchor of the Swiss franc on the euro. To answer this question, we focus on the origins of fluctuations in the exchange rate of the Swiss franc with a structural VAR model. Our results show that Switzerland would not have interest in adopting a hard peg with the euro. If the choice of such monetary regime may reduce the Swiss franc/euro volatility in the short-term, it would be accompanied in the medium term by significant sunk costs.