Irish Prime Minister Bertie Ahern called it "a very successful" EU summit.
EU leaders paid tribute to Bertie Ahern's diplomatic skills
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The two-day meeting in Brussels is the last before the 10 new member states join the club on May the first.
The big breakthrough was the decision by all 25 government leaders to re-start the stalled talks on a European Union constitution.
Mr Ahern said everyone at the meeting had shown the political will needed to get agreement by June for a constitutional treaty that should provide the basis of the way the EU works for at least the next 20 years.
The leaders are committed to putting their names to a text by the time of the next scheduled EU summit, on 17 and 18 June.
Motor
It is a dramatic reversal of mood, following the last top-level EU meeting last December, at which the constitutional talks collapsed amid bitter recrimination.
The shock of the train bombings in Madrid two weeks ago, which killed nearly 200 people, led to a sombre mood at the Brussels meeting.
One unforeseen consequence of the bombings was an electoral swing in Spain.
Outgoing Prime Minister Jose Maria Aznar had formed a political alliance with the government of Poland.
Both countries were determined to hold on to the preferential voting rights they had been awarded in the last major round of negotiations.
France and Germany, claiming to form the joint "motor" of the EU, insisted on a new and much simpler voting system for the enlarged EU.
It would mean that most EU laws would be decided by a "double majority" - that is, a majority of member states, providing that they represent 60% of the population of the whole union.
Personal touch
Spanish Prime Minister-elect Jose Luis Rodriguez Zapatero has not yet formed his government and was not present in Brussels.
But his off-stage commitment to an early accord on the constitution lifted the chances of an overall accord.
Another factor was the patience and skill shown by the Irish government, which holds the chairmanship of the EU until the end of June.
Other summiteers paid tribute to Bertie Ahern's way of building up consensus by person-to-person diplomacy.
There may yet be serious political turbulence ahead. Mr Ahern reckons there are about 15 points of dispute in the planned constitution.
Peace call
The summit also addressed the issue of terrorism and reflected on the situation in the Middle East.
Using unusually strong language, the EU leaders expressed their deep concern over extra-judicial killings by Israel, especially that of Hamas leader Sheikh Ahmed Yassin.
They also repeated their condemnation of what they called terrorist atrocities against Israelis, and renewed their commitment to an Israeli-Palestinian peace settlement based on a two-state solution.
On Iraq, the European leaders managed to set aside previous public disagreements to set out a positive vision of the country's future.
They speak of signs of international consensus over Iraq and look forward to the United Nations playing a vital and growing role, through a new UN Security Council resolution.
And they united in condemning what they call terrorist attacks which have disrupted Iraq's political and material reconstruction.