For the US capturing Saddam Hussein is only part of the problem
It's a man hunt. Thousands of American soldiers are looking for Saddam Hussein.
Tracking down the former Iraqi leader - dead or alive - would be a huge psychological boost. Next on the list come his two sons, Qusay and Uday.
In his home town, Tikrit, US troops are everywhere - in the air, on foot patrol, listening, watching and waiting.
If Saddam Hussein is still alive he may well be here in his heartland.
Saddam's personal secretary, Abid Hamid Mahmud al-Tikriti, is now in custody and he is talking.
But is he telling the truth? Who knows.
The word on the street is that finding Saddam Hussein will not be so easy.
"I don't think so," says one local.
'Net is closing'
"Saddam Hussein is a very smart guy. Sometimes his wife doesn't know where he's living, so even capturing Abid Hamid doesn't mean they are closer to Saddam Hussein."
Quite the contrary, say the Americans. The net is closing. They will find out the truth.
But local hostility is a significant obstacle. However hard they try, they are not winning many hearts and minds.
In the house where Abid Hamid was found by US troops, the reaction is typical.
They don't like the Americans and they don't want them in Tikrit.
Upstairs, the floor and the walls have been scorched by stun grenades, used when a special unit of troops stormed into the house in the dead of night.
"I blame the Americans", says Kaki Awad. "If they had come to our house and knocked on the door, that would have been fine, but they came in like animals."
We're not going to allow former regime members or anyone else to deter us from what we need to do
US Lieutenant Colonel Bill Macdonald
Across the room, her brother-in-law, Kayralla Awad, nods in agreement.
He's just been released from American custody.
"If Saddam Hussein came to your house", I ask, "would you offer him refuge too?"
"Of course", he says, "because of our Arabic tradition of hospitality".
"Would everyone round here do the same thing?"
"Absolutely. Any Iraqi, any Arab would do the same".
Not really true. Not any Iraqi. There are plenty of people in this country who are overjoyed that Saddam has gone.
But here in Tikrit, the graffiti on the main street says it all.
"Saddam exists," it proclaims, "And you can't buy Iraq with your dollars". Bush and Blair get only curses.
The Americans, though, are prepared to be patient. They only need one cast iron lead, one informer.
They've already seized the family jewels, more than five hundred pieces including diamond encrusted pendants holding Saddam's picture, thick gold chains and pearls the size of marbles.
In the same hoard, they found an identity card belonging to Saddam's wife, Sajida.
But where is the man himself? American officials in Washington say they are checking DNA samples from a convoy bombed last week near the Syrian border.
It may be more in hope than expectation. Until firm evidence emerges, they are working on the assumption that Saddam is alive.
The US military in Tikrit is now ensconced in the massive palace complex which Saddam Hussein built here on the banks of the River Tigris, a monument to privilege.
Lieutenant Colonel Bill Macdonald believes local attitudes will change.
"You've helped the school, you've helped the hospital, you've been a part of cleaning up an area that didn't have a lot of privilege before," he says.
"And you see the smiles on the kids' faces out there, then you know you did the right thing, and we're not going to allow former regime members or anyone else to deter us from what we need to do."
But the kids still chant Saddam Hussein's name when a foreigner walks by.
Maybe things will change, but as long as the Americans are here they will attract hostility.
Catching Saddam Hussein is only part of their problem.