Switzerland and the EU are negotiating again after a sudden break following a 2014 anti-immigration vote that called for preferred treatment of Swiss citizens. The country’s bilateral agreements with the EU include a so-called guillotine paragraph: if one agreement is broken, all the others lose their validity.

In other words, should the Swiss government insist to go against its agreement with the EU over the free movement of people, everything would have to be renegotiated, and Switzerland’s access to the single market would be in peril.

The EU insisted on its four principles, which according to Leuthard can mean long negotiations. Two years was an "extremely optimistic" estimate for Brexit, the president said, adding that the EU might have to think of additional provisions to the Treaty on European Union to sort out the situation.

Asked for comment on the situation created by the migration crisis, Leuthard said that Switzerland's humanitarian tradition and ability to help had been behind the decision to receive 1,500 refugees under the EU's migrant relocation plan, and over 10,000 more by means of granting them asylum or protection, as well as lowering visa requirements e.g. for family members.

Salaries in Switzerland were high, and the country attractive also for people who did not need help, Leuthard pointed out. With those they were very strict, and did not grant them the right to stay.

Leuthard's last stop was the e-Estonia Showroom, where she was introduced to the X-Road system behind Estonia's e-government services. Though the Swiss were very cautious about data protection, she would like to see some of the services introduced in Switzerland as well, in particular in healthcare, Leuthard said.