The Bush administration has dubbed Iran part of an "axis of evil", yet there is a widely-shared feeling that it has no clear policy towards the regime.
US policy is, for now, to work with allies, the European Union, Russia, Japan, to put pressure on Iran to accept more stringent inspections of its nuclear facilities.
US options range from engagement with Iran to the aggressive pursuit of "regime change
The Iranians have not rejected the idea, but seem to be trying to exact some kind of price.
But supposing they accept? The underlying problems between the US and Iran, over its alleged links with terrorism, its opposition to the Middle East peace process, and its suppression of human rights, would remain unresolved.
So, what policy options might the US choose to pursue? The choices range from engagement with Iran to the aggressive pursuit of "regime change".
Engagement would mean the pursuit of a dialogue with the Iranian Government, and a willingness to give it some inducements to modify its behaviour.
This option is favoured by one of Washington's elder statesmen, the former Democratic Party Congressman Lee Hamilton.
"I think that, while we have to keep uppermost the nuclear-weapon component of our policy, at the same time we ought to try to engage Iran on some of these difficult issues," says Mr Hamilton.
"That engagement would have to be done very carefully, very cautiously. It would probably have to be a conditional engagement. But I think over the long run it would have some hope of improving the relationship. We ought not to put all of our eggs in the regime-change basket."
Mr Hamilton takes issue with the hawks, both inside and outside the Bush administration, who believe the Iranian regime is irredeemable, and has to go.
"The high-point of recent 'neo-con' thinking would probably be the destruction of Saddam's statue"
This is the view of the radical Republicans known as the "neo-conservatives", or "neo-cons".
Joshua Muravchik, a prominent neo-con of the right-wing think-tank, the American Enterprise Institute, thinks that the goal of regime change in Iran is at least clearly implicit in what the Bush administration is trying to do.
"This is both in the rhetoric about the "axis of evil" and in the formal national security strategy paper that the president issued last September," says Mr Muravhick.
That was the paper which set out what has come to be known as the "Bush doctrine" of pre-emptive, or more accurately, preventive, action against perceived threats to the US.
A few of the neo-cons favour military action to remove what they see as the threat posed by Iran, for example, through strikes against its nuclear facilities.
But most think military action too risky and prefer a mix of pressures designed to weaken the regime, and encourage dissent.
A key question, however, is whether the neo-conservatives are in the ascendant, or have passed their peak.
"If you had to mark the high point, the high tide, of neo-conservative thinking in this administration, in a post-9/11 world, it would probably be the day the statue of Saddam Hussein came down in Baghdad."
Biding their time
Michael Hirsh is a senior editor at Newsweek and author of a new book on US foreign policy.
"Since 11 September, what we have seen looks very like a quagmire in terms of the post-war rebuilding (of Iraq). And it's become clear that the neo-conservative agenda is rather limited," he says.
"It focuses on regime change. It postulates the idea that countries and peoples so deeply want to embrace this Reaganite revolution of democratic and open-market transformation that they'll rush to do it on their own. And, of course, that has not been the situation since the war ended. I think the bloom has come off the neo-con rose, to some degree, and I think the direction of the Bush administration's policy is very much at issue now."
For the time being, US policy regarding Iran appears to be in limbo
But if the neo-cons have been temporarily weakened, they are certainly not out of the game. They are determined and influential people, and there are some in Washington who feel they are biding their time, waiting for George W Bush to win a second term in next year's presidential elections.
If he is re-elected, then, in the view of Raad al-Kadiri, Middle East expert at the Washington-based energy consultants, PFC, the neo-cons will be ready to push forward their agenda on Iran.
"Rightly or wrongly, they see in Iran a country that is on the edge, a country that requires a simple push and will actually undergo transformation from within, and that is what they're aiming to achieve.
"But this isn't something that's going to be quick or something that you're likely to see shouted from the rooftops until (George Bush's) second term. Put very simply, in terms of US domestic politics, regime change in Iran is not going to win a presidential election."
There is speculation in Washington that the neo-cons' preferred option would not be an Iraq-style invasion of Iran, but destabilisation through covert action. This would be highly controversial in Washington and among America's allies, who favour multilateral pressure on Iran rather than dangerous unilateral adventures.
For now, US policy is in limbo, but sooner or later the policy-makers will need to decide whether they want to negotiate with the Iranian mullahs in order to change their behaviour, or isolate and bully them in the hope they fall from power.
Read more from Roger Hardy in this series on Iran and the US: