By Paul Reynolds
World affairs correspondent, BBC News website
Gen Petraeus spent two days giving evidence to Congress
US President George W Bush plans to cut the number of troops in Iraq by 30,000 by July 2008, leaving a large force remaining - with no plan as yet for further withdrawals.
The cutback is the result of two factors.
Firstly, the current level of troops simply cannot be sustained because of strains on service personnel.
Secondly, the US commander in Iraq, General David Petraeus, says the current tactics are working and that the reduction can be made without sacrificing those gains already made or expected in the coming months.
So the 30,000-strong reinforcement that started to flow in February and reached its peak this summer will be taken out.
Some 130,000 US troops will, under current conditions, remain in Iraq, a level that anti-war Democrats in Congress say is too high.
The hope of Gen Petraeus is that the troops will increasingly be used to help Iraqis take the lead and that the American role will eventually be reduced to what the coalition describes as "overwatch". As that happens so the numbers can be cut.
He offers no timetable for this process.
No decisions on further withdrawals will be made before March 2008. Unless Congress intervenes Mr Bush will probably see out his term in the White House, ending in January 2009, with US troops levels in Iraq remaining substantial.
He would leave it to his successor to work out how to bring the troops home.
If the surge had not "worked", the administration would have been in crisis because troop levels would have been reduced anyway.
The reason for this emerged vividly in an exchange at the Senate Foreign Relations Committee on Tuesday between Gen Petraeus and Senator Jim Webb of Virginia.
Mr Webb, a Democrat who opposes the Iraq war, was once a marine. His son is currently one.
After pointing out that the improvement in Anbar province was not really connected to the surge but to tribal leaders, the senator complained bitterly that the tour of duty in Iraq had gone up to 15 months.
Soldiers and marines then got only 12 months off active service instead of the "two-for-one" policy that existed before - that is, you received twice the amount of time off that you spent on active service.
"We have this policy," said Senator Webb, "which has resulted in... a situation that I personally... have come to believe is very perilous to the well-being of the volunteer army, its system, the voluntary military system and to the well-being of these people, just the plain well-being of these people.
"The British in Iraq had a policy of four-to-one: six month employment, two years back [from Iraq]. The policy right now, particularly on the [US] army side, is three-quarters-to-one."
He then got this admission from Gen Petraeus: "That is something that very much informed my recommendation."
However, this factor was hardly mentioned in the general's written reports to the congressional committees. Instead the emphasis was on the success of the surge policy.
Eyes now shift to Congress.
It seems that for the moment, Mr Bush has the initiative against his critics there and may once again be able to stave off demands for a timetable to withdraw.
Democrats are looking at some other ways of influencing policy - for example by setting limits on the length of tours for the military in Iraq.
Whether Gen Petraeus really thinks he is being given enough time is not known. He co-wrote the US army manual on counterinsurgency, of which this operation is the first major test.
The manual stresses the long-term nature of the commitment.
He would probably have preferred the reinforcements to stay, but senior generals are political animals as well and Gen Petraeus has had to tailor his suit to the cloth available.