Switzerland is the EU's largest trading partner after the United States, coming in ahead of China and Japan, but the intertwining of multiple sectoral agreements makes the relationship difficult to manage.
The Helvetic Confederation is pushing for a third round of bilateral treaties to govern its relations with the EU, dubbed 'Bilateral III'. But the European Union wants a more comprehensive agreement and automatic acceptance by Berne of changes to EU legislation, which the Swiss say would go against the principle of sovereignty.
"Our country is at the heart of the European Union, but institutionally we are a third country, which considering our intense political and economic ties, makes the management of our relationship a constant challenge," Calmy-Rey conceded after the meeting, adding that any changes to that relationship would need to respect Swiss sovereignty.
Barroso described the meeting as "constructive and fruitful" and said both parties agreed on the need for a general overarching framework governing the bilateral relationship.
"The system of bilateral agreements is complex and heavy to manage," he said, echoing Calmy-Rey. "We are convinced that it is time to give a new impulse to our partnership," he added, explaining that companies and citizens deserve a level playing field and clearer rules.
Swiss citizens voted against joining the European Economic Area in 1992 and EU membership talks were consequently suspended. Since then Switzerland's dealings with the EU have taken a decidedly bilateral track. Two series of sectoral agreements, negotiated in 1999 and 2004, resulted in ten treaties that align a large portion of Swiss law with that of the EU (see 'Background').
But the process is not automatic like the one that governs the EU's relationship with other members of the European Free Trade Association, of which Switzerland is a member.
EU-Swiss relations are dealt with in more than 120 sectoral bilateral agreements, which require long and extenuating negotiations before they can be finalised and ratified as treaties.
According to diplomatic sources, both the EU and Switzerland are convinced that agreement needs to be reached as soon as possible.
Barroso and Calmy-Rey said they had made progress on the basis of parameters identified by 11 experts in a working group set up last year to find workable solutions.
"We are going to do this technical work as quickly as possible so that our relationship can be reinforced," said Barroso.
On 14 December, EU foreign affairs ministers called for an overhaul of the current system of bilateral treaties with Switzerland, which they said had ''clearly reached its limits''.
But sources told EurActiv that concessions on both sides will have to be made. "I don't see how Switzerland could make concessions to the EU if there is no progress on the issues that are dear to the Swiss. On the other side, the EU does not want to make concessions if Switzerland does not make progress on issues like taxation," said sources.
Another sacred issue for Switzerland is sheltering its sovereignty, "otherwise we would not be in a position to ratify the agreement," said Swiss diplomatic sources, before adding: "But surely a formula can be found."
Customs control agreement: A solution?
One example is an agreement to facilitate customs control, aimed at simplifying as much as possible customs procedures for goods traffic and at coordinating co-operation at border posts. That is seen as a possible model for other agreements.
The agreement was signed in 2009 and includes an obligation to notify in advance goods traffic between the EU and Switzerland and governs the modalities of further co-operation between Switzerland and the EU in the area of security.
It remains to be seen, however, when a clear framework will be adopted. Sources say the issue must be resolved as soon as possible, as Switzerland is to hold federal elections in October.