Bremer is among a handful of people to have visited the former Iraqi dictator in captivity. But how could Bremer be so sure he had Saddam and not one of his doubles?
Hours before the world knew about the capture, the American administrator and Lt. Gen. Ricardo Sanchez led four Iraqis to Saddam's cell to verify his identity. They are the only witnesses to see Saddam in captivity and reveal what the fallen dictator had to say.
"He looked to me like a man who had lost hope. You could see it in his eyes, particularly. He was tired, obviously, but beyond that, underneath that, you could see resignation ... He was a defeated man, thank God," says Bremer.
Saddam didn't know who the U.S. civilian administrator was, but he did recognize Dr. Mowaffak Al-Rubaie of the Iraqi Governing Council.
"I said, 'Saddam Hussein, may God curse what have you done to the Iraqi people. How are you going to face God in the here after, in the day of judgment? What are you going to say to God?' He just turned his face to the other side," says Al-Rubaie, who had been imprisoned by Saddam and tortured.
Al-Rubaie was one of the men from the Iraqi Governing Council who was brought to Saddam's jail cell right after he was captured.
"I found him … very defiant, very unrepentant," says Al-Rubaie. "He felt absolutely no remorse towards the crimes he has committed against the Iraqi people. Very unapologetic."
And, the unapologetic Saddam insisted he was still the people's choice.
"He was saying that he was an elected ... people have elected him to rule Iraq," says Al-Rubaie.
"I said, 'There are hundreds of thousands of people out in the streets now, rejoicing and celebrating your capture. Shall we take you and hand you over to these people? They will eat you alive, Saddam Hussein.' He said, 'These are thugs, hooligans, gangsters.'"
The meeting lasted little more than half an hour. But it's likely no one had treated Saddam like that in 35 years.
"I said, 'Why did you kill hundreds of thousands of people in the mass graves?' He turned around and said, 'Did you ask their relatives, what they had done these people? They were thieves, or they escaped from the battlefield,'" says Al-Rubaie.
He also questioned Saddam about the 1988 nerve gas attack on ethnic Kurds in northern Iraq. Saddam, however, told Al-Rubaie that the Iranians had poisoned the people of Halabjah with nerve gas.
At times, according to Al-Rubaie, Saddam was swearing in frustration.
"The 'F words' and the 'B words.' When he gets cornered with a question, and there was no answer, he looked at us, and he looked away and was swearing," says Al-Rubaie. "Physically [Saddam] was fit. But, psychologically he was ruined -- very demoralized, broken, irritable but mentally he was very with it."
The former builder of palaces was being kept in a small building believed to be in Baghdad.
"It's not a jail. He's not in prison. He was not chained, he was not chained to the bed," says Al-Rubaie.
And, the Americans were in the strange position of protecting Saddam from his own people. "I can tell you … he felt much safer with the Americans than us," adds Al-Rubaie.
Bremer says Saddam is being kept in solitary confinement, in a private room in a secure location: "I'm not going to go into details of how he's held. He's held in accordance with international rules and he's well treated."
Is he on suicide watch? "We keep watch over all prisoners under the circumstances, nothing special here," says Bremer.
But there is something special about Saddam's cell in that secure location. One American who has been inside told 60 Minutes that the walls are covered in white tiles. On one wall, there is a poster that shows the faces of the 38 former Iraqi officials who have been killed or captured.
They include the pictures of Saddam's two dead sons, Uday Hussein and Qusai Hussein. On the opposite wall of Saddam's cell hangs a portrait. Saddam Hussein now spends his day looking at a picture of President Bush.
Bremer, however, says the capture of Saddam has helped American intelligence tremendously, especially into the resistance -- but that he wouldn't describe the former Iraqi dictator as cooperative.
"I can just tell you there's plenty coming out and we're taking action on it," he says. "I'm just talking about the intelligence value from having him and the access to the things that were with him. But I wouldn't go into that in detail."
Terrorists tried to kill Bremer the week before Saddam's capture. His armored car was targeted by a bomb and gunfire. No one was hurt. From Saddam's former palace in Baghdad, Bremer told 60 Minutes that security is just one of his problems.
"We're dealing with a country whose infrastructure was devastated, not by the war, but by 35 years of economic and political incompetence," says Bremer.
"We don't have enough electricity in this country. Even though we are at pre-war levels of electricity generation, it still means we only meet two-third of the demand … We have to fix that by spending money -- American taxpayer money -- which we will do here over the next couple of years to get power generation equal to demand.
"The same goes for health care, water, gasoline, refineries, for the oil production. It is a comprehensibly mismanaged economy that we now have to fix. You don't fix something that was broken for 35 years in six months or eight months or a year. It's going to take time."
When they finally put Saddam on trial, Al-Rubaie says there will be no doubt that Saddam Hussein was a tyrant: "He can employ the most competent legal firm, lawyer, in the world if he likes. If he can't, the new Iraq, the new government of Iraq, will help him in employing the most competent legal firm in the world to defend him, because we believe this trial is going to be the trial of the century."
It may not be until that trial that the world hears from Saddam Hussein again.
Who has the last word?
"I had the last word. I asked him, 'Saddam Hussein, when you were captured by the Americans,' and I pointed to General Sanchez and Ambassador Bremer, 'When you were captured by them, you did not shoot a single bullet against them. You claim to be an Arab brave man. You are a coward. You had two Kalashnikov, AK-47s, machine guns and a pistol on his hip," says Al-Rubaie.
"'You did not shoot a single bullet. And you ask people of Iraq to fight. When it comes to your life, you can sacrifice all Iraqi lives, but when it comes to your life, you spare that ... Saddam Hussein, you are a coward.'"
And what did Saddam say? "He said, 'Have you fought in your life?' I said 'Yes, I have fought in my life,'" says Al-Rubaie. "Where? I said I fought in Kurdistan and in Iran. He shut up. He did not utter a word after that."
Al-Rubaie says he didn't want to leave the room that held Saddam captive: "I honestly did not want to leave. I wanted the meeting to be longer. I wanted to ask about other crimes he committed against Iraq, and my colleagues were basically encouraging me, and they left the room, and so I was the last one with Saddam. And I said, 'Saddam Hussein, may God curse you in this life and in the hereafter.'"