Professional mediators say there are some disputes you just can't resolve.

George W. Bush's conflict with Saddam Hussein may be one of them.

"This whole process has not been reassuring from a mediator's point of view, " said Charles Doran, executive director of Mediation Works, a Boston dispute-resolution firm. "I kept listening for diplomatic openings. Instead, all I heard was posturing and threats."

That hasn't changed over the past few days. On Monday night, President Bush charged the Iraqi leader with "decades of deceit and cruelty," and gave him until tonight to go into exile or face the wrath of the U.S. military.

Hussein responded Tuesday by saying he isn't going anywhere. He warned that U.S. forces will be met by an Iraqi soldier "behind every rock, tree and wall."

While mediators acknowledge that Hussein almost certainly has violated disarmament accords stemming from the last Gulf War, they say the White House has given him no room to explore a peaceful settlement to the situation.

"It appears that it was never the intent of the Bush administration to have a meaningful negotiation," said John Bickerman, whose Washington firm, Bickerman Dispute Resolution, has handled arbitration for some of the world's biggest companies.

"It's always been this administration's position to depose Saddam Hussein," he said. "That doesn't leave a lot of room for talks."

Is Hussein contractually obligated to disarm? Legal experts say that's debatable because he wasn't actually a party to United Nations resolutions calling for destruction of his various weapons.

"But if he did have contractual obligations, that sets up an even better case for mediation," said Merri Baldwin, a San Francisco attorney specializing in contract law. "It gives the mediator something to work with."

Still, corporate mediators emphasize that the only way a dispute can be resolved short of out-and-out warfare -- whether waged in court or on the battlefield -- is if both sides are willing to at least discuss other options.

"They've got to want to resolve it," said Steve Rosenberg, a Mill Valley mediation lawyer who also teaches mediation techniques at the University of San Francisco. "Otherwise, there's no reason to begin talks."

He and other mediation experts say that even if neither side in a dispute is willing to make the first move toward settlement, there must at least be an openness to meeting with a neutral third party.

Kofi Annan, the U.N. secretary general, would in theory be the best person to initiate such a move, and in all likelihood, he did send feelers to both Bush and Hussein.

For whatever reason, though, a U.N.-brokered mediation effort never got off the ground.

Meanwhile, with Bush repeatedly insisting that other nations "are either with us or against us," virtually no other world leader was able to approach the dispute from a position of relative neutrality.

"Who is there that Bush would listen to as a mediator?" asked Rosenberg. "The power balance is all out of whack."

Mike Kasperzak, head of Dispute Resolution Specialists, a Mountain View corporate arbitration service, observed that if the U.S. and Iraqi sides had been serious about finding a peaceful solution to their differences, they'd have done everything possible to meet at the negotiating table.

"The Camp David accords (between Egypt and Israel) resulted from both sides recognizing that something has to be done," he said. "They wanted to work things out, but they needed some help.

"One of the fundamentals of mediation is that it's a voluntary process," Kasperzak added. "The parties come to the table because they want to reach some resolution."

He and other professional mediators took the absence of talks between Washington and Baghdad as a sign that neither side in the conflict had an interest in seeking common ground.

"Without a willingness to negotiate, even the best mediator in the world couldn't accomplish anything," Kasperzak said.

Had Bush and Hussein agreed to hash things out, though, each mediator interviewed said the first step would be to get past their harsh public pronouncements and ascertain their true agendas.

If for Bush this means disarming Iraq while at the same time guaranteeing a steady supply of oil, so be it. If for Hussein this means accepting international treaties without ceding autonomy, fine.

The next step, mediators say, would be to narrow differences between the two sides by determining where compromises can be made and how much flexibility both parties are bringing to the equation.

Dana Curtis, who teaches mediation at Stanford Law School, said a good first step would have been to convene a panel of eminent figures to help define the key issues. "I would have included Jimmy Carter, Nelson Mandela and George Bush Sr.," she said.

Bush Sr.? The man who led the last war on Iraq?

"Maybe Bush Jr. would listen to him," Curtis reasoned.

With Bush and Hussein having each invested so much personal capital in their respective positions, an especially tricky task for any mediator would be coming up with a solution that would allow both men to save face.

"It would have been helpful if both leaders had said that peace is in their nation's interest," said Doran at Mediation Works. "Instead, they've created a juggernaut that makes war seem inevitable."

Bickerman, the Washington mediation specialist, said one of his toughest assignments came last year, when he brokered a pact between the Justice Department and Boise Cascade for the wood-products giant to reduce emissions at eight plants.

"The negotiations were very difficult," he said. "They took a long time. In the end, though, Boise Cascade was willing to make a number of concessions."

How does that compare with the conflict between Bush and Hussein?

"There's no comparison," Bickerman replied. "It doesn't look like the Bush administration has ever been willing to negotiate this thing."