By Roger Hardy
BBC Middle East analyst
The UN Secretary General Kofi Annan, continuing his mission to the Middle East, is in Jordan, where he will have talks on Thursday with King Abdullah.
Annan's Middle East tour is aimed at bolstering the fragile truce
From there he will go on to Syria and Iran to discuss their relations with the Lebanese militant group Hezbollah and other difficult issues.
But the mission is proving a particular challenge.
Mr Annan must have known this would be a thankless mission.
While there is a certain war-weariness on both sides of the Lebanese-Israeli border, the current ceasefire is fragile.
The main parties want the UN to play a role, but on their own terms.
The Lebanese want UN help in persuading Israel to withdraw its forces and lift its air and sea blockade.
UN investigations into Hariri's death point to Syrian involvement
On Wednesday Mr Annan failed to budge the Israeli Prime Minister, Ehud Olmert, on either count.
Mr Olmert has his own wish-list.
He wants the UN to secure the release of the two Israeli soldiers seized by Hezbollah in July and to stop arms flowing across the Syrian border to Hezbollah.
The Palestinians, for their part, want Mr Annan to persuade Israel to lift the closure of Gaza and open crossing points.
He must listen patiently to everyone's demands, in the knowledge that his ability to meet any of them is sorely constrained.
Road to Damascus
Even tougher meetings lie ahead in Syria and Iran.
Mr Annan, unlike the Bush administration in Washington, feels it is important to talk to both.
Iran nuclear ambitions are topping the agenda once more
Both are allies of Hezbollah. Both have the power to help or hinder his efforts to bring peace to Israel and Lebanon and the wider region.
But both have their own demands.
Bashar al-Assad, the Syrian President, resists the idea that the UN international force should police his border with Lebanon to stop arms getting to Hezbollah.
Anxious to avoid a dispute with its Syrian neighbour, the Lebanese government has said its own armed forces will do the job - an idea Israel will not find reassuring.
The fact is that Syria has benefited from Hezbollah's success in surviving its month-long battle with Israel - and has no interest in seeing it weakened or disarmed.
Moreover Mr Assad may set an unacceptable price for his co-operation.
The continuing UN inquiry into the killing of the former Lebanese Prime Minister, Rafik Hariri, has pointed to the possibility of high-level Syrian involvement - something Syria strongly denies.
On this sensitive issue, the Syrian president would dearly love to get the UN off his back.
Mr Annan's agenda in the Iranian capital Tehran is scarcely plain sailing, either.
He wants Iran, like Syria, to exert a restraining influence on Hezbollah.
He will also urge Iran to comply with the demands of the UN Security Council and suspend the enrichment of uranium - or face the possibility of sanctions.
Since the Israel-Lebanon ceasefire, the Iranian nuclear issue has once more risen to the top of the international agenda.
All the signs are that Iran will insist it is entitled to continue with a nuclear programme it maintains is purely peaceful.
Keeping the ceasefire alive may be the most the UN secretary general can realistically hope to achieve.
Balancing the competing demands of half a dozen Middle East leaders may be beyond his power, and perhaps his patience.