The European Union has told Switzerland that it is comfortable with discussing a special deal which restricts the rights of Europeans to settle in that country, even if this encourages Britain to demand similar concessions from the EU.
"We've moved closer on some points," said Mr Jean-Claude Juncker, the head of the European Commission, the EU's executive body, after talks with Swiss officials earlier this week. He added that he was "more optimistic" that negotiations were moving in "the right direction" on what he called a "Swiss-specific arrangement". Swiss President Johann Schneider-Ammann was also positive about the chances of a deal, telling journalists: "I am confident we can do it."
The upbeat note has surprised analysts, who assumed that, with negotiations over Britain's departure from the EU now looming large, Switzerland would find it difficult to conclude a beneficial deal on sensitive matters such as immigration, since each concession given to the Swiss could also be demanded by the British. But EU officials appear to have concluded that it is in Europe's interest to decouple the problem of Switzerland from the UK.
Switzerland has always been an oddity. Surrounded by the EU and utterly dependent on trade with the continent, the country has repeatedly rejected EU membership and obtained instead a special arrangement which provides it with full access to EU markets, but in return, obliges the Swiss to open their borders to the free movement of European citizens.
The snag is that this has resulted in a large inflow of workers from poorer EU states: foreigners with permanent residence now account for almost a quarter of the nation's 8.3 million residents. In addition, 300,000 Europeans commute across the Swiss border each day to work in the country.
Immigration is the chief topic in Swiss politics, a matter of key importance in a country which mandates nationwide referendums on most policy questions. In February 2014, the Swiss people voted in favour of imposing limits and quotas on immigration, in direct violation of the existing Swiss-EU deal.
The Swiss government was given three years to implement the immigration restrictions, but although the deadline is about to expire, little progress was made, largely because the EU had no interest in discussing the matter.
Earlier this year, Swiss President Schneider-Ammann flew all the way to Mongolia in order to catch up with the visiting Mr Juncker, but was granted only 45 minutes of his precious time.
The EU's reluctance to discuss such matters was understandable. Freedom of workers' movement is a cardinal European principle on which the EU has never compromised, and special pleading from Switzerland, one of the world's wealthiest nations, attracted little sympathy.
Once Britain voted to leave the EU, matters got even more complicated, for the Brits want exactly the same thing as the Swiss: all the benefits of European trading markets, with as little immigration as possible.
But Mr Juncker now seems to have radically reversed course, touting the possibility of a special Swiss deal after all.
One explanation for this surprise about-turn is that the Commission has realised that locking itself in an intractable dispute with Britain and Switzerland at the same time will only reinforce the impression of a continent in crisis, precisely what everyone seeks to avoid.
A public dispute over immigration with two nations is particularly tricky, since the demand for the restoration of border controls could well spread to other EU nations. The European Commission therefore has an interest in containing this debate, and forging a deal with the Swiss reduces the risk.
But the most important reason Mr Juncker feels relaxed about making some concessions is that he will demand a heavy price for it.
The EU is asking Switzerland, in return for its getting some caps on immigration while keeping access to EU markets, to accept that its domestic laws will change constantly to harmonise with EU rules, and decisions of EU courts will be automatically enforceable in Switzerland.
In effect, Mr Juncker has transformed the Swiss negotiations from a potential weakness into a source of strength for the EU: the Swiss will get part of what they want on immigration, but only by giving up even more of their sovereignty.
This is a principle which, if established, will serve as a grim warning to Britain as it negotiates with the EU.
It is a shrewd strategy, but also a dangerous one. For any deal which the Swiss government signs with the EU will have to be ratified in another referendum in Switzerland.
And the Swiss are good at saying "No" in all four of the country's official languages.