BBC correspondents say a semblance of normal life is returning to three Iraqi cities plagued by looting and violence since Saddam Hussein's regime crumbled.
Baghdad by Caroline Hawley
For the first time since American troops took over Baghdad, ordinary people are now beginning to venture out onto streets that were the preserve of looters.
Some shops have reopened, local religious leaders have been trying to recover looted goods, storing them in mosques until they can be returned.
Baghdad residents are beginning to venture outside
People who fled the war are now coming back to Baghdad but many are still angry at the Americans for allowing the chaos of the past few days, and some demonstrated in central Baghdad.
Several people demanded that US forces look for relatives they believe are still locked up in underground jails.
Others wanted water, electricity, jobs and for the Americans to stop looting that is continuing in some areas.
Basra by Rupert Wingfield-Hayes
The situation in Iraq's second city Basra is calmer on Sunday.
British troops occupying the city have today begun putting local Iraqi police back on the streets, to try to bring some order and to stamp out the violence and looting.
Outside the charred remains of Basra's former police headquarters, a group of about 100 men gathered in the morning heat, waiting to be inducted into Basra's new police force.
In Basra, the people want supplies as well as peace
Some wore the old green uniforms of Saddam Hussein's police, but most did not. They were too afraid to put their old uniforms on, they told me, as it would identify them as having worked for the old regime.
While this is being dubbed as a new police force for Basra, the fact is all of the men being recruited today once worked for the old regime.
British commanders admit that with their own troops stretched to the limit, they have little choice but to re-employ police, who until a week ago worked for Saddam Hussein. How they will be greeted on the streets is another question.
But the people here are desperate for some semblance of security.
At night the ripple of machine-gun fire can still be heard across the city, and there is still not a single shop open.
The looting has died down, but many people here will tell you that is simply because most of the good stuff has already been taken away.
Most of the city also remains without electricity and consequently without running water. Until the security situation can be improved, none of that is likely to change.
Mosul by John Simpson
For the moment at any rate, the crisis here seems to be over.
American soldiers are at last patrolling the streets of Mosul in some numbers and as a result the shops are starting to reopen and something like normal life is beginning to return.
People in the city are ascribing some of the credit for all this to the Islamic clergy.
Looted goods have been returned to a Mosul mosque
Many mullahs and imams broadcast appeals for calm and for an end to looting.
And in the street leading to one mosque in particular, people have been bringing back goods that were stolen and piling them up in the street.
It is a remarkable turnaround in a short time since, even during the night, there was a wild outbreak of shooting that lasted half an hour and an American soldier was shot outside the main hospital, where the looting and the violence has been greatest.
But now there are even one or two uniformed policemen on traffic duty in the streets.