By Roger Hardy
BBC Middle East analyst
US forces have pulled back from some of their positions around Falluja, amid reports of an agreement to end the month-old stand-off in the Iraqi city.
Falluja has suffered greatly during the fighting
The reported agreement - details of which remain vague - comes at the end of a month in which more than 120 US soldiers and an unknown number of Iraqis have been killed.
The Falluja agreement may or may not resolve one of the most pressing problems the US faces in Iraq.
But it comes at the end of a terrible month.
The twin stand-offs in Falluja, the staunchly Sunni city west of Baghdad, and in the southern Shia holy city of Najaf, have shown how far the security situation has deteriorated.
A year after the fall of Saddam Hussein's regime, the US-led occupation forces have alienated large numbers of Iraqis.
US officials have sought to portray their enemies as a small minority of troublemakers out to wreck the country's progress to democracy.
But most experts warn that disaffection is growing - and that heavy-handed military action will make matters worse.
US officials on the ground have followed two tracks.
They see the two insurgencies as a direct challenge to their authority so they have talked tough in public.
US forces have threatened to kill Moqtada Sadr, who is hiding in Najaf
They have repeatedly threatened to crush the Iraqi and foreign fighters in Falluja - and to kill or capture the radical Shia cleric Moqtada Sadr, who is holed up with his supporters in Najaf.
But an all-out assault on either city would carry daunting political risks.
So officials have quietly kept open indirect lines of communication with the very people they have publicly denounced as "thugs and terrorists".
A looming deadline
The events of the past few weeks have raised unsettling questions.
Has the Pentagon relied on too few troops to stabilise post-war Iraq?
Have its forces, especially in Falluja, ridden roughshod over local sensibilities?
Have its attempts to make the security forces more Iraqi - to replace foreign forces with newly-trained Iraqi police, soldiers and paramilitaries - been too hasty?
And, crucially, can US administrators meet their self-imposed deadline of 30 June for the handover of power to an interim Iraqi government?
They remain fully committed to that date - now just two short months away.
They know they have always been engaged in a race against time in Iraq.
Only by restoring some form of Iraqi self-government can they hope to convince Iraqis that further violence would be self-defeating.
Politics and security are intertwined.
The Brahimi plan
The spate of violence has pushed the US to rely more on UN envoy Lakhdar Brahimi
The escalation of violence has put added pressure on the US to rely on the UN special envoy, Lakhdar Brahimi, to help put a new government in place.
Mr Brahimi wants to set up a caretaker government of technocrats by the end of May - a full month ahead of the deadline.
But as he himself has been reminding everyone, the transition is unlikely to be smooth.
The prevailing insecurity is scarcely providing the right climate in which crucial political decisions need to be taken.
Moreover, the Bush administration still seems unwilling to relinquish the driving seat, though it is anxious for help from the UN and from other countries.
Its critics warn that without a real change of approach it will find it hard to get a new resolution which legitimises the transition through the UN Security Council.
And without a meaningful handover of power, already sceptical Iraqis may conclude that 30 June is a sham.