Under pressure from France, and others, to move more quickly in handing power back to the Iraqis, the Americans are trying to show flexibility - without relinquishing their own dominant role.
Their aim is to get a new constitution drafted by the spring and then approved in a referendum, thus paving the way for elections later in the year.
The message to the Iraqis is: You will be running your own affairs soon, but the transition must be handled with care.
Religious and ethnic groups want to be fairly represented
The task of supervising the drafting of the constitution is in the hands of the Iraqi Governing Council, the group of 25 Iraqis set up by the Americans in July as a step towards self-rule.
The Council has in turn set up a constitutional committee.
The committee's task is highly sensitive. Some experts think even six months may prove insufficient to iron out all the problems.
- Will Iraq be run by a single strong leader, under a presidential system? Or by a collective power-sharing leadership? If there is a president will he (or less probably she) be elected by the parliament or the people?
- How will parliament be elected? One man/one woman, one vote? Will seats be allocated according to proportional representation (PR)? Or on a winner-takes-all basis?
As a prelude to elections, the aim is to conduct a population census. But how feasible is that, given the prevalent insecurity in many parts of the country?
- What will be the role of religion in the new Iraq? Will it follow secular or Islamic (Sharia) law?
Will there be federalism, as the Kurds are demanding? If so, how would the country be divided?
Would local militias become unconstitutional? And if so, how would this be enforced?
Sects and secularism
Many of these are the familiar practical issues any country has to deal with in drawing up a constitution.
But Iraq presents special difficulties, because the overthrow of an all-powerful and repressive regime has left a gaping political void - and also because of the diverse character of Iraqi society.
Any new system needs to avoid stirring up sectarian or communal tension.
There are concerns about Iraq's deteriorating security situation
The Shia Arabs, comprising 60% of the population, want to be fairly represented - for the first time - in the Iraqi state.
Sunni Arabs, once the dominant political elite, need to be reassured they will not be marginalised.
Religious and ethnic minorities want their rights protected.
Given the new and stronger role of religion in Iraqi life, secular Iraqis are fearful of new restrictions on their lifestyles.
It is clear that the Americans want to offer the Iraqis a political "horizon" - in other words, a clearly defined transition to democratic self-government.
Among other things, this would give the Bush administration an exit strategy.
Less clear is whether the US-led administration, and its Iraqi allies, can complete this difficult transition in little more than a year.