Falluja was a necessary, but not a final operation in the plan by the United States and the interim Iraqi government to establish control over the whole country.
By Paul Reynolds
World Affairs correspondent, BBC News website
After Falluja, where next?
The guerrilla war is at a high pitch and other cities have yet to be fully pacified - Sunni-dominated Mosul in the north and Ramadi to the west of Falluja among them. Let alone Baghdad.
And proper civilian rule in these places has to be established.
Not an end
Falluja does not end this war. The insurgents will try to regroup.
The next few weeks will show whether they are successful or whether the stick of superior American firepower and the carrot of elections can diminish the rebellion.
The insurgents are reckoned to number about 20,000 but nobody really knows. In September, an American general said there might be 40,000 of them. This is no small insurrection.
The operation demonstrated a new determination by US commanders and the interim Prime Minister Iyad Allawi. They will not repeat the mistake they made earlier this year in handing over Falluja to the rebels.
The threat meant that the safe haven of Falluja could no longer be tolerated.
They will argue that their tactics are working, that they pacified the Shias mainly by negotiation and are ready to pacify the Sunnis by fighting as well.
Certainly, the Americans fought cleverly in Falluja this time. Advance warnings might have let the rebel commanders escape. But they also allowed civilians to get out and this has lessened the adverse impact of the fighting.
The marines also mounted initial diversionary attacks from the south, attracting the rebel fighters there, while in fact the main assault came from the north. The fighters were in the wrong place and became trapped.
But the US marines who took Falluja back might be reflecting on the meaning of their commander-in-chief's statement of 1 May last year that "major combat operations in Iraq have ended."
The elections, due on 30 January, are an essential element of pacification. A great deal is riding on them. But as they get closer, how much they will achieve becomes harder to discern.
They too are likely to be a milepost and not the destination. A fully constitutional government is not due to be elected until December of next year.
Iraq's Deputy Prime Minister Barham Saleh has even said that the January vote might not go ahead if the security situation does not permit. But he is a Kurd and his caution might be born from fear that the Shias will dominate the assembly, especially if the Sunnis boycott the elections.
Much work now needs to be done to bring the Sunnis on board. The Muslim Scholars' Association, a Sunni organisation, has called for a boycott, but it has also supported the insurgency, so perhaps its position is no surprise. Such opinion will have to be won over. And time is getting short.
Been here before
Historians of Iraq are recalling that in 1920, Falluja was a symbol of Iraqi opposition to British rule.
Juan Cole, professor of history at the University of Michigan, whose online column comments daily on Iraq, has quoted T.E. Lawrence, no less.
In August 1920, Lawrence wrote in the Sunday Times: "The people of England have been led in Mesopotamia into a trap from which it will be hard to escape with dignity and honour. They have been tricked into it by a steady withholding of information. The Baghdad communiqués are belated, insincere, incomplete. Things have been far worse than we have been told, our administration more bloody and inefficient than the public knows."
The British eventually imposed order and a king on Iraq. This time it is supposed to be different.