Two things happened on Wednesday which have given Washington and London some reason for hope in Iraq - but many other things must happen before that hope can be realised.
By Paul Reynolds
BBC News Online world affairs correspondent
Will President Bush's upbeat mood last?
First, there was the appointment of the interim Iraqi government which will take over on 30 June.
Second came the presentation of a revised draft Security Council text, which could form the basis of a new resolution giving UN approval to the plan.
The emergence of the interim government saw President Bush in a more upbeat mood than he has been for a long time when he came into the sunshine in the Rose Garden.
He declared that it "brings us one step closer to realising the dream of millions of Iraqis, a fully
sovereign nation with a representative government that protects their rights and serves their needs".
The White House, therefore, hopes that this is a watershed.
As for the resolution, it still needs some work done, but it seems that there could be an agreement.
Concessions have been made. The authority of the interim government over security has been stressed (though this still has to be fleshed out in a detailed agreement) and an end is foreseen to the mandate for the presence of the foreign troops in the "multinational force".
Ideally, the US and UK would like the resolution approved by the time of the D-Day celebrations on 6 June, and certainly by the start of the G8 summit in the US on 8 June. The Western allies could then present a united front after their deep divisions.
A word, though, of caution. The draft does not actually set a date for the withdrawal of foreign troops. It states that the mandate for the troops will expire on the "completion of the political process".
The completion of the process is due on 31 December 2005 when a fully, directly elected Iraqi government is supposed to take office.
Ending a mandate and withdrawing are not quite the same things, because the Iraqi government could always ask the force, or some of it, to stay. After all, US forces in Europe stay at the request of governments not under any UN mandate.
However, in the public mind, the two might become confused and thereby conjoined, thereby creating an expectation that the troops will be home in early 2006. Not a bad thing, you might think, for a US president on the election trail or a British prime minister under pressure.
It turns out incidentally that the phrase is in an existing UN resolution, 1511 from October 2003. Why it was not in the first draft this time round is a bit of a mystery.
The Foreign Office in London says it was "not considered necessary" and adds that it was put back into the latest draft "to create confidence that the multinational force is there to support the political process".
If it had been there from the start, a lot of trouble might have been avoided.
However, before London and Washington start bringing out the old metaphors about "turning the corner" in Iraq, there are many obstacles to overcome.
It was rather surreal to watch the assembled members of the government gather for their family photo while outside the bombs were going off. So will this government be able to get a grip on security?
It hardly seems possible in the few months it will be in office. An interim, appointed government is a start on the road to representative government, but it hardly carries a banner around which all can rally.
The best hope is that the new government will make local deals, as happened in Falluja, to calm things down while it builds up its own strength. Meanwhile, the multinational force should play less and less of a role.
That appears to be the intention. Already there is talk of US troops being reconfigured to protect the new government, not to attack insurgents.
Then one looks ahead to the next stage, which is December or more likely January, when elections are held to a National Assembly.
Even then, there will not be a directly elected government, for it is the Assembly which will choose a "transitional" government. But at least there will be elections.
The "transitional" government will surely provide a better test of how Iraq is doing than the present very weak structure. But it means another six months and more of uncertainty.
And it's not over then. The transitional government will have to prepare a new constitution by August 2005, hold a referendum in October and full elections in December. Only on the last day of December 2005 will a proper government take over.
That day is a long way off.