By Mike Wooldridge
BBC world affairs correspondent, Baghdad
A joint operation to improve security in Baghdad is bringing results, American and Iraqi officials say.
Thousands of extra US and Iraqi troops are in Baghdad
There has been a dramatic drop in violence in areas of the capital where house-to-house searches have been conducted, the officials say.
An Iraqi general has told the BBC he believed the securing of Baghdad was now not so far away.
But he also called on the Iraqi government to persuade militias to give up their weapons.
The Americans and the Iraqi government have put thousands of extra troops on the streets to wage this battle against insurgents, sectarian forces, and what they openly call death squads and violent criminals.
In the present phase of the operation they are working their way through the districts most prone to violence, cordoning them, searching house-to-house for illegally held weapons and preparing to hand over these areas to the police.
This battle of Baghdad, America's ambassador to Iraq says, will determine the future of the country.
In the eastern part of Baghdad for which he's responsible, Gen Bashar Mahmood Ayoub said the number of killings and kidnappings has been reduced a lot in the past month.
The Americans say this too.
A key issue has been whether there would be active political support from the government for reining in the militias, blamed by many Baghdad residents for much of the sectarian violence of recent months.
General Ayoub said terrorists played a double role, sometimes carrying out violence in the name of militias, though he accepted that both Shia and Sunni militias carried out acts of violence too.
"We need the help of the government," the general said, "to convince the militias to disarm."
Politicians should act and not allow themselves to become part of the sectarian violence."
He maintained that the Iraqi army had the capacity to protect Baghdad but couldn't do so alone for now.
And he accepted that the army had a job to do in building public trust in the police - widely seen as influenced by sectarianism.
Overall it's an assessment shared by the Americans, who say that while there may be a dramatic drop in violence in some neighbourhoods at the moment, it's a concern that some of the death squads might simply have moved elsewhere to escape the security net.