(CBS) CBS News Correspondent Jim Axelrod is embedded with the 3rd Infantry in Baghdad, where he filed this report.

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The 3rd Infantry's first brigade hit Saddam where he lives, or rather, at least one of the places he lives -- the Abu Guyrab palace. The palace is set on a square kilometer on the west side of Baghdad.

"It's great actually, to know we are in someone's house and he doesn't want us to be here," says Pvt. Daniel Dunn.

The soldiers expected to have to fight their way in, but the place was deserted.

"It's a great feeling first of all. Almost sickening, all this opulence. To take it away and give it back to the people it belongs to," says Col. Will Grimsley.

As soldiers look at the marble, the crystal, the huge rooms, the sweeping grounds, one has to keep in mind that this is just one of dozens of Saddam's presidential palaces.

The soldiers sit in chairs and laugh. Clearly commanders on the ground are feeling confident about the direction of the war. This was a poke in the eye mission -- taking Saddam's throne and making fun of a painting showing him directing his troops.

"If he's been directing this, he's not any good at it," says Grimsley.

While the 1st brigade walked untouched through the front door of this palace, the 2nd brigade drove downtown by sites like the Ministry of Information and the Tomb of the Unknown Soldier while toppling a statue of Saddam Hussein. Today is about symbols as much as power as some of the regime's biggest and most ornate dominoes are falling.

"I think it shows we're close," to the tail end of the war says Lt. Col. Rock Marone.

This was the start of the week in Baghdad. If the commanders are right, by week's end this could be a very different city.

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