Later this week, European Union leaders - minus one country - will meet in Bratislava. The Slovakia summit will be the first to take place without the UK. But Britain will loom large in discussions, as Europe grapples with Brexit.
The mood of EU leaders is understandably sombre. German Vice-Chancellor Sigmar Gabriel spoke for many when he warned that Britain must be shown that it cannot keep "the nice things" about the EU without paying a price. Any other approach, he said, would leave the bloc "in big trouble".
Emotionally and politically, Mr Gabriel's approach is understandable. Nonetheless, it is a mistake. Rather than treating Brexit as a threat, the EU should treat it as an opportunity. The process of negotiating a new relationship with Britain should be used to address the many other problems afflicting the union.
More specifically, it is now clear that Britain is not the only current member of the club that is unhappy with the high level of political integration involved in belonging to the EU. Just last week, the Visegrad Four - Hungary, Poland, Slovakia and the Czech Republic - issued a demand for a looser bloc, with some powers returned to nation states.
The negotiations around Brexit should be used as an opportunity to create a two-tier EU that meets these concerns. The first tier could press ahead with much closer political integration, pursuing the longstanding goal of "ever closer union" in Europe. The countries on the second tier would restrict themselves to participation in the single market and cooperation on foreign and security policy.
This two-tier approach could potentially meet the needs of both federalists and Eurosceptics. The federalists have long complained that Britain has acted as a drag on deeper integration. But suspicion of the idea of "political union" is now widespread across the bloc.
The anti-federalists include not just the Visegrad Four, but also probably the Irish, Dutch, Swedes and Danes. If those countries were to opt for the outer tier, the remaining federalists - such as Germany, Belgium, Italy, Spain and (probably) France - could press ahead with deeper integration.
Creating two tiers of membership would allow the union as a whole to continue to fulfil its two most important missions: preservation of the single market and the projection of European interests on the world stage. A two-level structure could also solve the Brexit problem, since the UK could probably slot quite easily into the second tier rather than leave the bloc outright. In time, even non-EU members such as Switzerland, Norway, Turkey and Ukraine might join the second tier.
Of course, there is plenty of "devil" in the detail. Countries and legal powers would not be placed neatly and obviously into the first or second tier. Would France go with the federalists or the anti-federalists? The answer might depend on the outcome of France's presidential election next year.
Could a country that has adopted the European single currency really opt for second-tier membership? That might be difficult given the degree of fiscal integration that the euro might ultimately demand.
The question of free movement of people would also be very sensitive. It is already clear that post-referendum Britain is highly unlikely to accept full-scale free movement of people from the rest of the EU. And there are also other union members that want to see some restrictions on free movement. The Dutch would like to see an "emergency brake" procedure, in which an individual country could restrict inflows of people from the rest of the EU if they exceeded a certain preset level. France is threatening to stop applying the EU law on "posted workers", which allows bosses to pay lower wages to employees seconded from other EU countries.
The difficulty is that while restrictions on free movement of people would be an important demand for the antifederalist countries in western Europe, the anti-federalists in eastern Europe regard the maintenance of free movement as a vital national interest.
Yet there is still plenty of room for creative negotiation in dealing with this issue. One possibility would be to adopt the Dutch idea of the emergency brake, preserving the substance of free movement while providing reassurance that immigration will not be unlimited. Another idea would be to make a much clearer distinction between free movement of labour and free movement of people, allowing full labour mobility within the EU, but restricting migration rights to those who have a job.
Many of the political class in Brussels would regard all these proposals as dangerous heresy. They want the union to hang on to all its current powers (the "acquis"), and to prove the folly of "leaving Europe" by making Britain's divorce as painful and as difficult as possible. But the idea that the EU is best preserved by treating it like Alcatraz - and demonstrating that anybody who attempts to escape will inevitably suffer a terrible fate - is not ultimately a good way of keeping the bloc together.
It would be far better for European leaders to acknowledge that some of Britain's complaints about the EU are quite widely shared. Rather than trying to preserve the current structures at all costs, they should design a new two-tier union that could, potentially, keep everybody happy.