For al-Hamdani, worse was to come. In his speech at the Amman conference, he said that the Americans had arrested and detained him in June 2003. Three months later he had been freed, only to see his Baghdad home come under U.S. attack: “There were eight persons in the house, four of them children. My family was terrified. I had no idea why they were shooting.” He says he gave himself up willingly, but a U.S. soldier pushed him to the ground, handcuffed him, then stood with a boot on his neck.

Al-Hamdani’s anger as he related these experiences was palpable, yet he remained, he insisted, willing to work with the Americans. “The impact was visceral,” says Clad. “The way he put it was that people treated the way he had been ‘had died in the eyes of their families.’ Raad had tears in his eyes, remembering the humiliation. Respect and honor are a crucial part of Arab culture, and here he was, reminding us that we had taken this away from him and his family.”

In front of the conference, Clad stood up and walked across to al-Hamdani. “What we did was shameful, it should never have happened, and we apologize unreservedly,” he said. “There was no intention to bring dishonor on your family.” All the other Americans present followed suit. Talal al-Gaaod had been telling his Sunni friends that the Americans, improbable as it might seem, could well be responsive to an overture. The apology to al-Hamdani looked like evidence he was right. “Word soon got round about this,” says Jones. “It definitely had an impact.”

Later that day, al-Gaaod asked Jones to arrange a private meeting. “He said, ‘There’s a fellow here who wants to talk to you,’” Jones recalls. A little later, Jones, Clad, Walker, and Colonel Roy David Harlan, the U.S. military attaché in Amman, gathered in Jones’s suite. With al-Gaaod was a man known as “the Messenger,” also called “Dr. Ismail,” a medical doctor and lawyer who had come to Amman from Fallujah. He was, al-Gaaod said, the designated representative of 16 Sunni insurgency groups. Walker had by now grown accustomed to frustrating meetings with people who claimed to be close to the insurgency’s leadership. In April of that year, after the Fallujah lynchings, says Walker, “there were no less than seven lines of negotiations going on with all manner of reputed ‘leaders,’” none of whom turned out to be real.

The Messenger, he says, was different. Walker had been studying Iraq’s tribal structures on the ground for months. As he told the Marines’ commander, Lieutenant General Conway, in an e-mailed report after the meeting, the Sunnis who had come to Amman “can roughly be likened to the Sinn Fein and the I.R.A. [in Northern Ireland] … One is attempting to work within the system and the other is fighting us on the battlefield.” In other words, says Walker, if Talal was the insurgency’s political face, the Messenger, in contrast, was its military face, “by far the most credible and important contact with the insurgency we had.” Jones agrees. “There was just no question that he wanted to make a deal with us. The insurgents had seen when we went into Fallujah in April what we could do, and they wanted to put a stop to this before any more of their cities were destroyed.” The Messenger, Walker says, told the Americans, “We are not your enemy. Al-Qaeda is your enemy,” and the U.S. and the Sunnis should be working together to defeat it.

The Messenger, says Jones, stayed at the conference after the meeting and showed up the next day with two men Talal identified as insurgency colleagues. They had brought a list of conditions the insurgents were demanding in return for ending the killing of Americans, written in the name of something called the Iraq National Resistance Council. The original document’s English was poor. Working through a translator, Clad and the Messenger produced an improved version. It began with three “non-negotiable points”—that Iraq “should be viewed as one united country”; that the occupation must end, “even if that has to happen in stages”; and that “the wealth of Iraq should be used for the benefit of Iraqis and should not be siphoned off by others.” To this was added a significant rider: “We don’t mind participation by American companies. As a matter of fact, we encourage their participation.”