By Jim Muir
BBC News, Baghdad
The one-day conference of Iraq's neighbours, attended by other interested parties including the Americans and British, seems to have passed off as well as anybody expected.
Iraqi PM Nuri al-Maliki (left) greets US ambassador Zalmay Khalilzad
It was the first formal encounter between the Americans and Iranians - who have no diplomatic relations - for more than two years. US relations with Syria are almost as bad.
Both countries are accused by Washington of fostering terrorism and enabling arms, fighters and money to cross their borders into Iraq - charges they deny.
This ice-breaking encounter seems to have gone down well all round.
The US ambassador in Baghdad, Zalmay Khalilzad, who led the US team, spoke later about the positive and businesslike atmosphere.
Despite controversy over contacts with the US, Iranian and Syrian newspapers on Sunday generally welcomed the outcome of the meeting.
Given the deep differences between those taking part, the potential for acrimonious wrangling was clearly there.
But according to those who took part, the atmosphere was positive even when some of those differences were aired.
"Issues were debated, but in a very respectful way," the conference host, Iraqi Foreign Minister Hoshyar Zebari, told the BBC.
"Everybody was concerned to accentuate the positive, not to issue provocative confrontational statements."
British ambassador Dominic Asquith, who headed the UK delegation, added: "It was a good meeting, with a very positive tone.
"All those who were round the table were clear in their emphasis of support for the government of Iraq and for the Iraqi people in their efforts to confront terrorism and sectarian violence."
From Iraq's point of view, one of the most important practical results of the meeting was agreement to set up security committees with the neighbouring states, with a brief to tackle the issue of cross-border infiltration.
Iraqi officials said they would be pressing to ensure that all sides lived up to the commitments given.
Iraq also seemed to attach much importance to opening a dialogue between the US and the UK on one side, and Iran and Syria on the other.
"The other important achievement was that Iraq became a forum for some lively exchanges between the US and Iran, as well as Syria and the UK, which really created a good and positive atmosphere," Foreign Minister Zebari said.
"Despite what you may hear about it being just a handshake and some formalities, it was much deeper than that, and it was all focused on Iraq."
"The chemistry was good, and there were some very lively exchanges both between them, and with others."
Iraq security talks have raised hopes of a thaw in US-Iran relations
Mr Zebari said that Iraq needed its neighbours' help to secure internal stability, and in return, could offer them a forum and an issue on which they could talk to the US and the UK.
While much of the interest was focused was on the situation between the US and Iran, British ambassador Dominic Asquith said Syria had also played a positive role.
"The Syrian participant was particularly constructive, indeed came up at the end with some compromise language for the final statement which received full backing, indeed applause, from everybody around the table, so there was a good spirit of constructive engagement and the Americans played their full part in that."
If this first encounter was positive despite the obvious limitations, what comes next?
One disappointment was that the participants were not able to agree on the timing, venue and level for the follow-up meeting that all agree should take place soon.
It had been hoped that there would be agreement on a conference at foreign ministerial level - including Condoleezza Rice - in April, possibly in Istanbul.
The Turks have offered to host such an "expanded" meeting.
But given differences over the agenda, scope and level of participation, the most likely scenario seems to be an initial meeting restricted to the foreign ministers of Iraq and its six neighbours, who would then decide whether to broaden it to include the permanent members of the UN Security Council and others.