American military planners at US Central Command here in Doha are working furiously on how to consolidate their forces' grip on Saddam International airport and on the wider strategy for seizing Baghdad.
The one thing the Americans are not going to do is to storm into the capital in a full-frontal military assault, which would have catastrophic effects for the population of Baghdad.
It will be a very delicate strategy of mixed elements.
We could see, for example, the use of slightly smaller, laser guided munitions directed at very specific targets - not the huge bombs that we have seen used elsewhere that could have very substantial results in terms of collateral damage - which means the killing of civilians.
We will see the use of air power and the deployment of special forces.
The Americans are prepared to take their time to an extent, but will not wish the operation to drag on.
The first task will, of course, be to secure the whole of Saddam International Airport.
The coalition still need to win hearts and minds
American troops will be going through this very large area - checking all the buildings and structures for booby traps or any small pockets of Iraqi forces that may still be in that area.
From a strategic point of view, we will almost certainly see it being used quite soon by substantial numbers of American troops.
There will obviously be an effort to secure the perimeter area - to make sure there are not Iraqi troops with perhaps shoulder-launched anti aircraft missiles that could bring down incoming aircraft.
It is possible that the American 101st Airborne Division, which has been doing other business in other parts of the country but is poised to join the battle for Baghdad, may decide to come in directly to the airport.
All the major access points to Baghdad will be controlled.
There will be checkpoints. Civilians who are just conducting their normal business will be allowed to move in and out.
The full strength of the Republican Guard has not materialised
Others, young men of military age, will definitely be the subject of scrutiny by the American forces who will be on those checkpoints.
Gradually, they feel, they will wear down the resistance by those inside the city who are loyal to Saddam Hussein.
We may be talking about many thousands of people - perhaps as many as 15-20,000 Special Republican Guard for example, but they hope that, ultimately, they will wear down the remnants of the regime to the point where people will recognise that it is simply not worth carrying on resisting.
As for the regular Republican Guard, there is a huge question mark about them.
Where are they ? Have they simply been decimated, have they melted away? Is there still an intention, perhaps, to use chemical weapons?
We simply do not know.
Hearts and minds
Operations in Baghdad will be similar to those in the southern city of Basra, where the British continue to nibble away at the defences there, to target the elements still loyal to Saddam Hussein where they can, when they can; to use a lot of psychological operations and propaganda.
We will see an awful lot of use of special forces, of psychological tactics - perhaps trying to interfere with the broadcasting on Iraqi TV so that people know, in their homes, that the Americans are coming.
Siege is a word you will not hear people using at CentCom - indeed, when you talk about sieges they say "No, no, no - this is not what we are talking about. The idea of encircling a city, of treating it like a Grozny or a Stalingrad, that is absolutely out of the question."
In Basra, it is worth remembering, the city remains to a certain extent quite open - with civilians free to move in and out.
That is something the British are very keen to preserve, while they go after the elements loyal to Saddam Hussein.
The Americans will wish to be no less careful, in Baghdad.