While many see agreement between the leaders as now more likely, there are serious concerns over what might happen next.
"I'm optimistic a solution can be found," says Greek columnist and commentator Evangelos Arteos. "But I'm pessimistic about what happens after that."
The latest phase of the talks comes after the failure of the first round to reach an agreement. Turkish Cypriot leader Rauf Denktas and Greek Cypriot President Tassos Papadopolous had met to negotiate a settlement based on the UN’s Annan Plan.
Named after UN Secretary General Kofi Annan, the plan foresees the reunification of the island after 30 years of de facto separation. And although earlier attempts to do so have failed, many are hopeful this time will be different.
"I'm optimistic because the process built into the Annan Plan is a smooth one," says Turkish commentator Fehmi Koru of the newspaper Yeni Safak, known to be close to the Ankara government. "Once the negotiating process has started, it can’t be stopped."
So, now Greece and Turkey, the island's two big brothers, will be directly involved in this second phase of talks, being held at the Swiss resort of Buergenstock.
Turkish Foreign Minister Abd Allah Gul and Greek Foreign Minister Petros Molyviatis are to try and fill in the many blanks left by the first round, before Turkish Prime Minister Recip Tayyip Erdogan and Greek Prime Minister Costas Karamanlis arrive on 28 March to give another push for settlement.
Rauf Denktash ( L ) and Turkish
PM Recip Tayyip Erdogan
If the four parties agree, then the settlement will be put to a referendum, held simultaneously on both sides of the island's divide on 20 April.
However, if no agreement is finalised, or if there are still points of contention, Annan himself will move to write the deal which will be put to the voters.
"What people here are saying now is wait for the outcome of the Swiss talks, and let’s see the final text," says Ozdil Nami, of the Turkish Cypriot Businessmen’s Association and a deputy for the largest Turkish Cypriot party, the Republican Turkish Party (CTP).
But there are still some major issues outstanding that may delay a settlement.
"There's a lot of concern here about two issues," Nami continues. "The first is the property issue, the second, cementing political equality in the new, reunited Cyprus between Turkish and Greek Cypriots."
Property is a great concern because following the Turkish invasion of the island in 1974, many thousands of Greek Cypriots fled their homes in the northern part of the island, which became de facto Turkish Cypriot territory.
Likewise, thousands of Turkish Cypriots also fled their homes in the southern, Greek Cypriot dominated part of the island.
"Property will be a very difficult issue to solve," warns Namil. "After 1974 too, Greek Cypriot land was sometimes given to settlers from Turkey, who then sold it on to others. What happens to the people now on that land isn’t clear."
Solving this will undoubtedly require financial compensation.
"The Turkish Cypriot side has always favoured a global exchange on this issue," adds Namil. "We always said we would compensate for loss of property and land. We will simply have to find the money to pay the Greek Cypriots for this."
But it is not clear where this money will come from.
"The US and the EU always in the past said they would sort this out, but now we feel they are backing off a little. This is making people here a bit uncomfortable."
Another major issue is that of "derogations".
"The main point on the Greek side is the derogations," says Arteos. "This is the point that worries Greece and the Greek Cypriots the most."
The problem is that Cyprus is due to join the European Union on 1 May this year. When it does, it will be subject to EU law, which includes the right to move freely within EU territory and to own property.
Cyprus is due to join the European
Union in May
However, under the Annan Plan, the number of Greek Cypriots who would be allowed to move back to areas now under Turkish Cypriot control has been limited. This contradiction between EU law and the agreement opens the agreement to legal challenges at some future date.
"This is a major problem for Turkey," adds Koru. "The EU must give assurances that the agreement can't be changed later."
Turkish Cypriots, who number only around a fifth of the island's population, are concerned that the areas of the island earmarked under the plan to contain Turkish Cypriot majorities will gradually come back under Greek Cypriot control if they are all allowed to move back.
Underlying all these issues though is perhaps most importantly, the question of trust – or a lack of it.
"Even if the sides reach an agreement and the Greek and Turkish Cypriots vote yes in the referendum, the problem will not be over," warns Arteos. "The plan needs good will to work, but there is no good will."
Turkish Cypriot leader Denktas has pulled out of the second phase of talks, as he is against the Annan Plan. Meanwhile, Papadopoulos is also not known for his support of the initiative.
"The plan needs good will to work, but there is no good will"
"They are both leaders from the old school," says Arteos. Denktas has been involved in Turkish Cypriot nationalist politics since the 1950s, while Papadopolous too has a decades-long pedigree of nationalist activism.
"Under the Annan plan, Papadopoulos may become president of a reunited Cyprus, with Denktas vice president. Yet, how can these two possibly work together?" says Arteos.
It is a worry now beginning to be voiced on both sides of Europe’s last divided nation.