Five states have big problems with the current document. France and the Netherlands, which held unsuccessful referendums in 2005, need to make changes to persuade their public that a new treaty is not the constitution under a different name.
Britain, the Czech Republic and Poland are concerned about losing sovereignty, while Ireland (together with Sweden) has not yet ratified the constitution. Germany and Italy are the two biggest members of the "Group of 18", which strongly supports the constitution.
Who are the "Group of 18"?
EU leaders gathered in Rome in October 2004 to sign the EU constitution. Eighteen states have so far ratified the document. Austria, Belgium, Bulgaria, Cyprus, Estonia, Finland, Greece, Hungary, Italy, Latvia, Lithuania, Malta, Romania, Slovenia, Germany and Slovakia passed it in their parliaments, while Spain and Luxembourg held successful referendums.
Having already received public approval for the draft constitution, the "Group of 18" generally want to keep as much of the document as possible. As current EU president, Germany wants a speedy deal to revitalise the EU.
What is the current voting system?
In most areas, new EU laws are approved when a "qualified majority" of states agree. Under the Treaty of Nice, votes were allocated in a way that boosted medium-sized member states' relative voting weight, giving Poland (27) almost as many votes as Germany (29). Ireland got seven votes.
In total, 345 votes were distributed to the 27 EU states, with a qualified majority set at 255 votes (73.91 per cent of all votes) and a blocking minority set at 91 votes.
To mollify large countries, states can demand that a decision has the support of states representing 62 per cent of the EU population.
What is the double majority system?
One of the key parts of the constitution is a new voting system for the Council of Ministers, the EU institution where ministers decide new EU laws. Under the "double majority" system, population size becomes the key determinant of voting weight.
Decisions would require the agreement of 55 per cent of states, representing 65 per cent of the EU population. Proponents say it is a more democratic and transparent system. But Poland vigorously opposes it because it reduces its own voting weight.
Warsaw has proposed a "square root" formula which says voting weight should be proportional to the square root of a state's population. It increases the relative voting weight of Poland and Germany.
What are enlargement criteria?
The Netherlands blamed "enlargement fatigue" as a factor in the failure of its referendum on the constitution and wants this area highlighted in a revised treaty.
It wants to incorporate the Copenhagen criteria in the new text. These are rules that define whether a country is eligible to join the EU, requiring a state's institutions to preserve democratic governance, human rights and a market economy. A reference to enlargement criteria in a new treaty could be seen as a snub to EU candidate Turkey.
What is a legal personality?
Under the constitution, the EU would have a "legal personality" for the first time and there are specific references to the primacy of EU law over national law.
States such as Britain and the Netherlands are concerned this undermines national sovereignty.
In practice, EU law already enjoys primacy over national legislation in areas such as environmental policy, where it has the power of co-decision.
But giving the EU a legal personality will enable the EU to enter into international agreements, thereby boosting its diplomatic power on the world stage. This has prompted major concerns in Britain.
Where does Ireland stand?
Ireland's small size relegates it to being a bit player in the talks. But a deal on the constitution was achieved under the Irish presidency and Taoiseach Bertie Ahern remains a firm supporter of the document.
The key for Ireland is the institutional compromise achieved in the constitution, which left taxation and defence a national competence. Ireland also fought hard to prevent large member states from gaining a permanent commissioner at the expense of smaller states.
This is one of the key reasons we oppose reopening the "Pandora's box" of institutional compromises that are laid out in the first part of the constitution, particularly the voting system.
Should national parliaments get a red card?
The Netherlands and the Czech Republic are proposing that a majority of national parliaments should retain the power to scrap commission proposals.
They are concerned about the creeping powers of the union and fear that a new voting system will make it more difficult to block EU legislation.
Under the constitution, national parliaments could ask the European Commission to redraft a proposal if a third or more objected to it.
The commission and European Parliament oppose strengthening this provision, believing it would significantly undermine their ability to act.
Will referendums be held on a new treaty?
The French and Dutch "no" votes in 2005 plunged the union into crisis, and led pro-Europeans to argue that the referendums were hijacked by national rather than EU issues.
France, Britain and the Netherlands in particular want to strip away the constitutional elements (name, symbols and new powers) of a new treaty to enable them to justify ratifying it in parliament rather than through a vote.
Ireland could be the only state to hold a referendum, a position mandated by the Crotty judgment in the Supreme Court in 1987. Denmark and the Netherlands both say they will study a final treaty to determine if a referendum would be required.
Will there be any new elements in a revised treaty?
In an effort to mollify the "Group of 18", who strongly support the constitution, and to take account of current events, states have proposed adding new elements to the text.
It seems almost certain that the fight against climate change will be mentioned in the new treaty, and the need to boost energy security is also likely to be included.
Some states are also keen to have a social protocol added to the text to alleviate concerns in some member states, such as France, that the EU is too liberal and market-driven.
Is there a danger of "two-speed Europe"?
Italian prime minister Romano Prodi has warned that states opposing the constitution and seeking to limit the new EU treaty's scope could prompt a "two- speed Europe".
Under this scenario, states that want closer integration would move ahead in vanguard groups, leaving behind those that were not ready to pool their sovereignty.
To a certain extent this has already occurred in areas such as justice and home affairs, where Britain, Ireland and Denmark have opted out of various elements.
But plans are already afoot in the commission to create vanguard groups on corporate tax policy. An unambitious treaty could provoke further division among the EU-27.