But even as they spoke, two more of their colleagues were reported killed in incidents in Saddam's heartland north of Bgahdad and near Mosul, where his sone Uday and Qusay died Tuesday in a ferocious gun battle with US forces backed by helicopter gunships.

"The Baath Party is on the run. It's just a matter of time, we're going to smoke them out," Major Josslyn Aberle told AFP in Tikrit, Saddam's home town 150 kilometres (93 miles) north of Baghdad.

"It's one step closer to going home, because of the psychological impact on the remnants of the regime."

In Baghdad, some troops patrolling the streets expressed a reserved optimism about their colleagues nabbing two of Iraq's most wanted.

"That works for me," Private Jeana Frederick, 18, told AFP, appearing nonplussed that the enfants terribles of the former regime had been eliminated.

Others in her unit said the troops exulted on learning that Tuesday's operation yielded the most important result since US President George W. Bush declared the war over May 1.

"There was a pretty wild celebration," said Sergeant Chris Clyburn, 25, from the state of Alabama. "It will build morale, especially for the Iraqi people."

The two sons were among the most reviled men in Iraq. Qusay was the seldom-seen heir apparent to the Iraqi strongman's throne and headed his dreaded security and intelligence apparatus, while Uday commanded the Fedayeen militia.

Their demise boosted hope that US troops could soon be wrapping up the most crucial part of their military operations.

"People are falling now, just like dominoes," said an Iraqi-American civilian contractor working with Clyburn's unit in counter-intelligence, who identified himself as Johnson Akhnana.

"It's a blessing."

Not all US troops were aware of the results of Tuesday's spectacular raid.

"For real?" said shocked Specialist Chante Bundy of the 501st military intelligence brigade, taking a few moments to process the news that the sons had perished.

"It shows we're doing something right out here," said the 22-year-old from Virginia.

One soldier, however, voiced concern that the stupendous firepower employed against the Husseins in Mosul thwarted any efforts to capture the fugitives alive.

"I don't feel that (killing) is the right answer for anything. It's better to capture them alive," said a somber Corporal Robert Myers, 25, also of the 501st.

Akhnana said such a successful operation was was long overdue.

"It will ease the criticism (of the US occupation) 100 percent," he added.

The killings were a much-needed shot in the arm for the floundering US reconstruction effort in Iraq, where citizens have grown increasingly resentful of the coalition's presence and the snail-like progress in restoring security and basic services.

"Now we're trying to work on something, to establish a government, get running water, sewage, electricity and health care," Akhnana said.

US officials, including the top adminstrator in Iraq, Paul Bremer, have likened the killing or capture of the trinity of Saddam and his sons as a mortal blow to the insurgency campaign, tantamount to cutting the head off a snake.

Yet Saddam Hussein's fate remains a mystery, despite a massive manhunt for the former dictator who vanished April 9 when his regime crumbled.

He has bedeviled American authorities by apparently issuing audiotapes in which he calls for resistance against US occupiers.

Yet Akhnana was more confident than ever that Saddam would be captured, saying there were now "very good odds" that US forces would eventually rope in their enemy.

WAR.WIRE