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Soldiers from the U.S. Army's 4th Infantry Division (search), who all but missed the invasion of Iraq but have been at the front line of postwar hostilities, spent Sunday afternoon smoking cigars after scoring the allies' biggest triumph since the fall of Baghdad.

"It almost seems too easy," Sgt. Ebony Jones (search) of Kansas City, Mo., said after his comrades captured Saddam Hussein. "This is the best thing that ever happened to us here."

Soldiers of the 4th Infantry's 1st Brigade Combat team found a downtrodden, bearded Saddam hiding in a coffin-sized underground bunker on a farm near here, Maj. Gen. Ray Odierno (search) said Sunday.

"The intimidation and fear this man generated for over 30 years is now gone," Odierno said in a statement. "A significant blow has been dealt to the former regime elements still attempting to hamper progress in Iraq."

In the division's headquarters in Saddam's hometown of Tikrit, two dozen soldiers gathered in front of a television, cheering as their unit's accomplishment began to ripple across the airwaves, quickly dominating the news.

No one on the base said anything about their mission winding down after such a big catch. Tikrit and the rest of the Sunni Muslim areas north of Baghdad -- the area under the 4th Infantry's control -- remain one of the toughest patches of Iraq, with or without Saddam, they said.

"His capture will show others that they cannot run and hide," said Sgt. Don Williams of Houston. "Attacks will not stop, but this will have significant impact."

"This is the real thing," said Pfc. Eric Gainly. "This is simply great, but it won't stop attacks. There are people who won't stop."

In nearby Adwar, where Saddam was captured Saturday night, Capt. Joe Munger of the 4th Infantry Division called the development a Christmas present. "I think it should put a swagger in people's step," he said. "Morale here is really good."

The 4th Infantry Division arrived to occupy Tikrit and the surrounding area in April, after the war had already wound down. The division's entrance into the war was delayed when Turkey denied permission for the United States to use its territory as a staging area for a thrust from the north. Consequently, the division saw almost no action during the invasion.

But as the occupation wore on, the area around Tikrit grew increasingly restive, and the 4th Infantry found itself in the center of the postwar action -- especially the hunt for Saddam and other top fugitives.

Alongside the hunts, the division has been cracking down on anti-U.S. guerrillas operating in its patch, by using tough tactics like sealing entire villages inside barbed wire cordons, demolishing homes and making incessant sweeps through towns and neighborhoods.

Odierno said those tasks would continue.

"The capture of Hussein only strengthens our resolve to continue the fight against those conducting anti-coalition activities," he said.

After sunset Sunday, the streets of Tikrit plunged into darkness and an eery silence. Soldiers on patrol in the city, recalling the increased insurgency after Saddam's sons Uday and Qusay were killed in a gunbattle last August, said they were being extra cautious.

"We must remain vigilant. We had an increase of attacks after we nailed Saddam's sons, it could happen again," said Sgt. Cesar Castro of 1st Infantry Brigade, 4th Infantry Division.

The soldiers also were waging another war against former regime's diehards -- a graffiti war.

After Saddam's supporters sprayed dozens of walls and suitable surfaces with slogans "Long live Saddam," one patrol added Sunday: "In jail forever."