By Crispin Thorold
BBC News, Baghdad
In Gen David Petraeus and Ambassador Ryan Crocker, the US administration has arguably its strongest leadership in Iraq since the invasion of the country five years ago.
Washington's key leaders in Iraq are due to report back
The commander of coalition forces in Iraq and the US ambassador to Baghdad are both highly educated, with years of service in the Middle East.
In Washington over the next few days they will have to draw on their experience and talents when they give
Congress their latest assessment of Iraq.
But there may be as much attention on the questioners at the Senate Armed Services and Foreign Relations Committees as on the men who are testifying.
All of the main contenders for president of the United States are expected to be in Congress. Senators John McCain, Hillary Clinton and Barack Obama are likely to echo the main concern of the American people: "When will our troops be coming home?"
Ultimately, the decision will be made by the next president but for now Gen Petraeus will say that he wants to continue to withdraw troops until they reach roughly the numbers that were in Iraq before the American "surge".
That should happen by July, when Gen Petraeus wants to freeze further withdrawals of American soldiers and review security.
The American strategy in the long term is to hand over control of the whole country to the Iraqi security forces. That may take some time.
The limitations of the Iraqi army and police were exposed in the recent fighting with members of the Shia militia, the Mehdi Army.
Shia militiamen have proved a formidable foe in recent weeks
The Iraqi forces, with their tanks, heavy weaponry and the support of coalition aircraft, faced tough resistance from militiamen fighting with machine-guns, mortars and rocket-propelled grenades.
The worst fighting appears to be over, after the Shia cleric Moqtada Sadr, who is the inspiration for the Mehdi Army, called his men off the streets.
This was a tactical withdrawal, not a defeat. The fighters still have their weapons and sporadic clashes continue which could develop into another round of widespread conflict.
The Americans have been keen to portray the fighting in Basra as a breakthrough.
"This was an Iraqi operation conceived, planned, executed by the Iraqi security forces under the prime minister's direction", said Ambassador Crocker at a recent briefing to journalists.
"There has been a lot of discussion on problems in planning and in execution, and that may be perfectly valid.
"But this, nonetheless, is still an undertaking that the Iraqis simply have not been able to embark on before."
One thing the fighting did prove is that the Sadrist movement cannot be defeated by military means alone.
There were many desertions in the Iraqi security forces. A government source says more than 1,000 soldiers and policemen refused to fight.
Instead, American and British forces were drawn into the clashes in Basra, Baghdad and many towns in southern Iraq.
The struggle for Basra was begun by the Prime Minister, Nouri Maliki, who spoke about the need to rid the city of "criminals and outlaws", but it was characterised by many as an ill-advised power grab by the Shia governing coalition against its political rivals in the Sadrist movement.
All of this comes ahead of provincial elections, which are due to be held in the autumn.
The American administration has pushed for the poll, but it may strengthen Moqtada Sadr, rather than weaken him.
Now Nouri Maliki is demanding that the Mehdi Army give up its weapons if it wants to contest the poll.
Despite the intra-Shia fighting, al-Qaeda remains "enemy number one" for the Americans in Iraq.
US soldiers are still backing up Iraqi forces on the ground
Al-Qaeda has faced setbacks since the surge began, but it remains a potent force in the north of the country, particularly in Mosul.
It was in that city that Gen David Petraeus made his name but it is now arguably his greatest challenge.
Since February, the Iraqi army and the Americans have been carrying out military operations against Sunni insurgents.
Many of the gains that have been made against al-Qaeda in other parts of Iraq are a result of a "tribal awakening".
Thousands of Sunnis are now fighting against al-Qaeda, rather than alongside them.
Sunni politicians want these tribesmen to be integrated into the Iraqi security forces.
That is starting to happen but the process has been slowed by the Shia-dominated central government, which remains suspicious of the armed Sunni groups.
From the beginning, the American administration has called for a "political surge" to accompany the increase in troop numbers.
Iraqi politicians have made some progress on issues like the reintegration of Baathists - former members of Saddam Hussein's government - into public life but critical issues like how to distribute oil revenues amongst different communities remain undecided.
A new president
The status of the oil-rich region around Kirkuk is also another potential flash-point.
According to the Iraqi constitution, a referendum on the future of the city should have been held by the end of 2007.
That has been delayed but the Kurds, who believe the city should be under their control, remain determined to push their claims.
This is the complex, often violent, background to the testimony that Gen Petraeus and Ambassador Crocker will give Congress.
The political and security challenges in Iraq are considerable but the general and the ambassador will be positive, if cautious.
These men can only advise the politicians on Capitol Hill about the future involvement of the US in Iraq.
US policy in the country will ultimately be decided by the successor to George W Bush.
And that is why the comments of Senators McCain, Clinton and Obama will be listened to as keenly as those of Gen Petraeus and Ambassador Crocker.