Tony Judt, the British historian of Europe, wrote before his untimely death last year that: “if we have learned nothing else from the 20th century, we should at least have grasped that the more perfect the answer, the more terrifying its consequences.”

In its desperate search for solutions to the sovereign-debt crisis, Europe has turned this logic on its head. The European Union has made of imperfection something of a way of life. Consensus-seeking has rounded Europe’s sharper edges and has prevented any of the more powerful players from high-jacking the political process. However, imperfection also means that the EU has primarily advanced thanks to a long series of compromises.

In the old days, an agreement such as the one sketched out at the latest European Council on December 9th would have been hailed as a big leap towards a more integrated Europe. British veto notwithstanding, a fiscal compact with automatic sanctions and binding rules on public finances would have been the toast of Europhiles for weeks to come.

Well, no more. Few independent voices today claim that this deal was decisive; even fewer dare to predict that the EU will come out of this crisis stronger than it was before. Instead, the EU is routinely blamed for producing half-baked and half-hearted solutions.

It is difficult to predict how long the fragile treasuries in the Eurozone periphery can sustain this loop of bloated expectations and underwhelming responses. But the more profound question arises: Is an imperfect organization based on accommodating differences and allowing exemptions suited to bring Europe out of the crisis?

A good answer may come from Denmark, which has taken over the rotating EU presidency on January 1st. Like other Northern European members, Denmark has kept at arm’s length from some of the more ambitious experiments of supranational integration. Copenhagen has negotiated for itself a number of opt-outs from the EU, notably in the fields of defense and security policy, justice and home affairs, and on joining the euro.

The current European quagmire would seem to vindicate this position; unsurprisingly, recent polls suggest that 63 percent of the population would vote against Denmark’s entry in the Eurozone. While the government has promised to hold popular referenda on the defence and justice opt-outs, it has no intention of putting the euro opt-out to a vote.

On the other hand, it is hard to deny that Denmark has benefited from being in the EU. For a small and open economy, which directs 70% of its foreign trade to the EU and EU accession countries, the Union’s huge market is vital. Moreover, the EU's imperfect construction has made it possible for Copenhagen to customize its membership.

Denmark more than any other country appreciates the perils of taking this customization too far. The British veto on financial regulation at the recent European Council is the latest example of a government persuaded that it is better off with less, or even without, Europe. Only last spring, the previous Danish government decided to reinstate custom controls at its borders as a way to combat organized crime. Whether or not it was in breach of EU legislation on the free movement of people, the measure instantly turned Denmark into the object of an international outcry, no different from Britain today.

In one of the very first moves since election in September, Denmark’s new centre-left government has performed a U-turn on the border control decision. Moreover, as the country’s new Europe minister announced, Copenhagen aims to act as a bridge-builder in Europe. Copenhagen’s special membership makes this a natural task, especially when dealing with an increasingly Euro-sceptic London.

But any such bridge is needed if it takes Europe somewhere. Until the financial markets started to meddle with Europe’s destiny, the dominating narrative in Europe was that “more Europe” is beneficial for the prosperity and well-being of individual European countries. As Prof. Judt implies above, anybody arguing in favor of closing borders or erecting trade barriers would be confronted with the specters of 20th century Europe.

Today, the tables have turned. If an unexpected influx of migrants crowds our borders, we are better off closing them. Similarly, it would seem obvious to most people if Germany opted to consolidate a smaller, virtuous Eurozone and then go it global on its own, backed by its commercial powerhouse.

It is a tough challenge for anyone to explain how an imperfect Europe is suited to solve the present crisis. It is even harder to explain why it is better to be inside rather than outside the EU. As one of the beneficiaries of Europe’s imperfection, Denmark is a good candidate to take up this challenge.