The June summit set the tone for the new treaty
Ministers from EU member states have launched a three-month conference to finalise the details of the so-called Reform Treaty, the replacement for the doomed EU constitution.
But what do people across the EU think of the revival of the constitution in a different form? BBC correspondents find out.
BELGIUM: OANA LUNGESCU
If anyone loves the European constitution, it's the Belgians. In the latest EU-wide Eurobarometer poll, a whopping 82% say they support it.
The Belgians top the poll - issued in June - while the British come at the very bottom, with only 43% saying they are in favour.
An overwhelming majority of Belgians also say they want more European integration and would gladly hand the EU greater powers over the environment, migration and social matters.
During the June marathon summit to thrash out a replacement for the constitution, Belgium's outgoing prime minister Guy Verhofstadt was among those EU leaders who fought a rearguard action against attempts by Britain, Poland and the Netherlands to claw back powers from Brussels.
When Belgium celebrated its national day at the weekend, the ceremony was opened by 27 youngsters carrying a huge EU flag - and the EU anthem was played before the Belgian one.
FRANCE: HUGH SCHOFIELD
It was France that first rejected the constitution at a referendum two years ago, but according to the country's new leader, Nicolas Sarkozy, this does not mean the country is anti-European.
Instead, he says, there was a widespread disillusionment with the course the EU had taken. He has therefore been at pains to reassure voters on the issues that most worry them.
The original text was widely attacked for enshrining free-market economics, so Sarkozy had "free and undistorted competition" removed from a list of EU objectives.
Polls showed a majority were against Turkish entry, so he argued against full membership for Ankara.
In his rhetoric on Europe, Sarkozy makes constant reference to the idea of "protection". The EU has to improve the lives of its citizens, he says. If the euro is too high and killing exports, for example, then politicians have a duty to talk it down.
All this sounds to sceptics more like "protectionism" than "protection", but it goes down well in France.
With the president continuing to enjoy high popularity ratings, there is every reason to expect the country to follow his advice and adopt the new treaty without demur. By parliamentary vote this time.
IRELAND: JAMES HELM
It would be an exaggeration to say people are on the edge of their seats worrying about the fate of the Reform Treaty, but Ireland's role in the development of the constitution has not been forgotten.
Back in 2004, it was Irish Prime Minister Bertie Ahern who got Europe's leaders to agree on the text, at the end of Ireland's six months running the EU's rotating presidency.
Down the years Ireland has been a pretty enthusiastic member of the European Union.
Due to the requirements of Ireland's own constitution, Irish voters will get to have their say in a referendum on the Reform Treaty.
It is likely to be held in the first half of next year, and a poll conducted back in April and May suggested fairly strong support.
The Irish government will be wary of complacency, however, remembering how in 2001, to almost universal surprise around Europe, Irish voters rejected the Nice Treaty.
Then, the Green Party helped lead the No campaign. Now, the Greens are part of a coalition government, so may be less likely to rock the boat.
THE NETHERLANDS: GERALDINE COUGHLAN
Dutch voters rejected the EU constitution two years ago, and about half of the electorate is still Eurosceptic. But there seems to be a growing recognition that a document is needed to bind EU countries together.
Eight out of 10 of the country's MPs support the idea of a constitution and believe it will enhance Dutch influence in Europe.
But Dutch people are thrifty - and being one of the biggest net contributors to the bloc, they want to see value for money.
A major concern for The Netherlands is that the Reform Treaty includes new powers for the EU in areas such as justice and home affairs.
There is uncertainty over whether this will threaten national sovereignty and transfer powers from governments to the EU.
There is still a possibility that the Dutch could hold a second referendum on an EU constitution. The idea is popular among the far-right and the far-left-wing parties, though the centre-right government is not keen.
POLAND: ADAM EASTON
Poland's conservative coalition government is much more Eurosceptic than the public.
In a recent survey, a full 89% of those questioned said they supported EU membership.
The country's accession to the EU in 2004 was seen by many here as the country finally taking up its rightful place in the heart of Europe - a place denied by Stalin's imposition of a Soviet-style communist system after World War II.
Public opinion on support for the new EU treaty has not been tested, but in a survey conducted after the rejection of the old constitutional treaty by French and Dutch voters in 2005, more Poles said they would vote for it than against.
Prime Minister Jaroslaw Kaczynski, who has described last month's summit agreement on the treaty as a great success, says he sees no threat to ratification of the treaty in Poland.
But his junior coalition partners have other plans. They have announced they will campaign against ratification.
So far, Mr Kaczynski has not announced any plans for a referendum, but if he does, the signs are it would succeed.
UK: LAURA KUENSSBERG
The EU treaty stirs plenty of passion in British politics but curiously the debate is less about what is actually in the draft, than whether the public will be able to vote on it.
Former prime minister Tony Blair said there would be a referendum on the previous version, the now failed EU constitution.
But his argument, now adopted by Gordon Brown, is that the new draft document is inherently a different beast, and doesn't transfer significant powers.
Mr Brown insists that the UK's "red lines" have been met: Britain will maintain control over foreign policy, tax and benefits, criminal justice and get an opt-out on a charter of fundamental rights.
So, he argues, no public vote is needed to approve the plan.
Not so, say the Conservatives. They argue the treaty is basically the same as the failed constitution, and surrenders powers hand over fist.
Even though polls suggest about three quarters of the public want a referendum, the government knows it wouldn't win.
It's easier, at the moment, for Gordon Brown to risk unpopularity by refusing to hold a referendum, than gamble on an embarrassing likely defeat.