To resolve a crisis in which the impossible has become possible, it is necessary to think the unthinkable. So, to resolve Europe’s sovereign-debt crisis, it is now imperative to prepare for the possibility of default and defection from the eurozone by Greece, Portugal, and perhaps Ireland.

In such a scenario, measures will have to be taken to prevent a financial meltdown in the eurozone as a whole. First, bank deposits must be protected. If a euro deposited in a Greek bank would be lost through default and defection, a euro deposited in an Italian bank would immediately be worth less than one in a German or Dutch bank, resulting in a run on the deficit countries’ banks.

Moreover, some banks in the defaulting countries would have to be kept functioning in order to prevent economic collapse. At the same time, the European banking system would have to be recapitalized and put under European, as distinct from national, supervision. Finally, government bonds issued by the eurozone’s other deficit countries would have to be protected from contagion. (The last two requirements would apply even if no country defaulted.)

All of this would cost money, but, under the existing arrangements agreed by the eurozone’s national leaders, no more money is to be found. So there is no alternative but to create the missing component: a European treasury with the power to tax and, therefore, to borrow. This would require a new treaty, transforming the European Financial Stability Facility (EFSF) into a full-fledged treasury.

But this presupposes a radical change of heart, particularly in Germany. The German public still thinks that it has a choice about whether to support the euro. That is a grave mistake. The euro exists, and the global financial system’s assets and liabilities are so intermingled on the basis of the common currency that its collapse would cause a meltdown beyond the capacity of the German authorities – or any other – to contain. The longer it takes for the German public to realize this cold fact, the higher the price that they, and the rest of the world, will have to pay.

The question is whether the German public can be convinced of this argument. Chancellor Angela Merkel may not be able to persuade her entire coalition of its merits, but she could rely on the opposition to build a new majority in support of doing what is necessary to preserve the euro. Having resolved the euro crisis, she would have less to fear from the next election.

Preparing for the possible default or defection of three small countries from the euro does not mean that those countries would necessarily be abandoned. On the contrary, the possibility of an orderly default – financed by the other eurozone countries and the International Monetary Fund – would offer Greece and Portugal policy choices. Moreover, it would end the vicious cycle – now threatening all of the eurozone’s deficit countries – whereby austerity weakens their growth prospects, leading investors to demand prohibitively high interest rates and thus forcing their governments to cut spending further.

Leaving the eurozone would make it easier for the most distressed countries to regain competitiveness. But, if they are willing to make the necessary sacrifices, they could also remain: the EFSF would protect their domestic bank deposits, and the IMF would help to recapitalize their banking systems, which would help these countries escape from their current trap. Either way, it is not in the European Union’s interest to allow these countries to collapse and drag down the entire global banking system with them.

The EU’s member countries, and not only those in the eurozone, must accept that a new treaty is needed to save the euro. That logic is clear. So the discussions about what to include in such a new treaty ought to begin immediately, because, even with European leaders under extreme pressure to agree quickly, negotiations will necessarily be a prolonged affair. Once the principle is agreed, however, the European Council could authorize the ECB to step into the breach, indemnifying it from solvency risks in advance.

Having in sight a solution to the eurozone’s sovereign-debt crisis would be a source of relief for financial markets. Even so, because any new treaty’s terms will inevitably be dictated by Germany, a severe economic slowdown would be almost certain. That might induce a further change of attitude in Germany, in turn allowing the adoption of counter-cyclical policies. At that point, growth in much of the eurozone could resume.