When the Prime Minister emerged from Downing Street on Wednesday night, he said: "Our objectives in this military action are clear: to degrade his capability to build and use weapons of mass destruction, and to diminish the threat he poses to his neighbours."
Minutes later, the President said: " Our mission is clear - to degrade his capacity to develop and use weapons of mass destruction or to threaten his neighbours."
The military side of the equation may be clear, but the political strategy is opaque, and deliberately so. The US and Britain are hoping that the air strikes will undermine Saddam Hussein, and clear the way for the military to topple him, but they know this is a gamble.
In the longer term, they know they may have to learn to live with the Iraqi regime. In that sense, the air strikes are both the last gasp of an old policy - containing Saddam through weapons inspections - and the first blast of a new one.
The old policy relied on four elements: weapons inspections, sanctions, a regional and international group of countries that were committed to containing the regime, and the threat of military force. Each is of diminishing value.
The weapons inspections, certainly, are over, a fact now acknowledged by Britain and the US. Indeed, it is arguable that the Unscom mission has been dead for over a year. "Unscom has been ineffective for some time," said Sandy Berger, the President's national security adviser.
So the most obvious reason for the strikes is to hit the known targets once and for all, knowing that there is little that can be done now within Iraq to prevent Saddam Hussein from secretly developing weapons of mass destruction.
Obviously, this course of action can not be repeated, especially given that the intelligence the West has will become gradually less useful. So what next? "We will pursue a long-term strategy to contain Iraq and its weapons of mass destruction, and work towards the day when Iraq has a government worthy of its people," said Mr Clinton.
Take the second part first: replacing Saddam. The covert efforts by the Central Intelligence Agency and the Secret Intelligence Service to topple the Iraqi leader have so far been farcical and disastrous. It is likely that the US and Britain hope that, by targeting units like the Special Republican Guard and the Special Security Service - key props of the regime, and the weapons concealment operation - they can open a window of opportunity for the Iraqi military to oust Saddam. But that is a pretty faint hope.
In the longer term, the US and Britain hope that Saddam will go, and that a better regime will emerge. "The hard fact is that so long as Saddam remains in power, he threatens the well-being of his people, the peace of his region and the security of the world," said Mr Clinton.
"The best way to end that threat once and for all is with a new Iraqi government - a government ready to live in peace with its neighbours. Bringing change in Baghdad will take time and effort. We will strengthen our engagement with the full range of Iraqi opposition forces and work with them effectively and prudently." The key word here is "time", something neither Washington nor London have any influence over.
So the longer-term plan has to involve thinking about life with Saddam for some years. The UN's "oil for food" programme will garner more resources for the regime, enabling it to improve conditions in the country and to help its supporters.
In a brilliant piece of analysis earlier this year, Anthony Cordesman, of the Centre for Strategic and International Studies, looked at the question of "Living with Saddam".
"Much as we may dislike tyranny, Saddam's regime is one of the most effective authoritarian regimes of modern times. Saddam may not be popular, but he is accepted and he is in control," he said.
Military force will clearly be a part of this long-term strategy. "We must be prepared to use force again if Saddam takes threatening actions," said President Clinton. "The credible threat to use force, and when necessary, the actual use of force, is the surest way to contain Saddam's weapons of mass destruction program, curtail his aggression and prevent another Gulf War.
"So long as Iraq remains out of compliance, we will work with the international community to maintain and enforce economic sanctions," he added.
But sanctions will be increasingly hard to maintain. Iraq will, without Unscom, be able to start replacing its military material and developing weapons of mass destruction. The message of the strikes is partly that Saddam is there, and will be there for some time.
That is why the strikes that are taking place are intended to do as much damage as possible: they are the beginning of what may be a long haul.Reuse content