I never thought I’d be glad to see them. But I was. And so are most of the Iraqis I’ve talked to. “Things are more quiet these last weeks,” a young baker explained to me this afternoon. He spread his hands as if he were smoothing the sheet on a bed. “I hope this is not the calm before the storm.”

I hope so, too. And if it’s not–if it really is a turning point toward peace and prosperity for Iraq–then there’s a simple reason: The quasi-sovereign government installed June 28 is playing politics Iraqi style. Sure there’s a lot of bluster and a fair dose of brutality. No doubt there’s plenty of corruption, too. But there’s also a feel for the mood on the street that the U.S.-run Coalition Provisional Authority, now defunct, never even began to have.

A first priority of the new government is to make the capital city safe and restore public services. That’s obviously what you’d want to do, right? But Proconsul L. Paul Bremer, based in the American city-within-the-city known as the Green Zone, lived in a world of self-serving denial every bit as delusional as that of his betters in Washington. His constant blather about free markets and democracy, mouthed in Iraq but meant to be heard inside the Beltway, was matched by a persistent failure to stabilize and revitalize Baghdad itself.

Iraqis remember too well that their capital city was surrendered virtually intact, and only destroyed in the days after the Americans rolled into town. The troops stood back while liberated looters stripped the infrastructure of the city to the bone. Since then, Baghdadis have watched with sheer incredulity the Americans’ inability to restore regular electrical service. They’ve learned to fear the ferocious, random firepower of the American soldiers patrolling their streets. At the same time, they’ve seen criminal gangs turn kidnapping into an industry. “People say the Americans wanted to make us suffer,” an Iraqi doctor who works in the air-conditioned Green Zone told me before going home to her sweltering, lightless home.

The new Iraqi interim government may not be able to solve all these problems, but at least it’s focused on them. And if it can focus on a few more, then truly there may be hope that Iraq will pull out of its death spiral, and Americans will pull out of Iraq.

The next step is the amnesty proposal due out this week. In an interview with The Financial Times, interim President Ghazi Yawer said, “We are offering a silky hand to law-abiding people, and we are offering a sharp sword to anybody who wants to be above the law.” Inside the Green Zone, the Stars and Stripes newspaper distributed to soldiers headlined the hard line: “Iraqi president announces crackdown on insurgents; Al-Yawer vows ‘sharp sword’ against militants”. But, in fact, it’s the silky hand that will be extended first to many Iraqis who’ve fought and killed American troops. “If it’s just the people of this city, some of them killed 10 soldiers, we are offering an amnesty,” said Al-Yawer. “We have to do that, we have to be brave enough to accept our people and embrace all Iraqis.”

Yeah, that quote makes me cringe, too. Amnesty for rebels who’ve killed five or 10 Americans? But Yawer’s just being realistic. The next crucial step is for this Iraqi government to start reaching agreements with the major tribes in the countryside, especially in the west, to end their role in the insurgency. A lot of them have been fighting what they see as a righteous battle against invaders, and taking revenge for their relatives who’ve died these last 15 months.

A key to the problem was the U.S. effort in March and April 2003 to kill individual Iraqi leaders with precision munitions. The smart bombs were guided by dumb people, as it turned out, who dropped them on the basis of execrable intelligence. In the go-go days of Iraqi Freedom, in mid-April last year, such respected reporters as Con Coughlin of Britain’s Daily Telegraph would quote their friendly intelligence sources’ claims that Saddam’s son Uday, the bespectacled diplomat Tariq Aziz and even the clownish information minister “Baghdad Bob” Sahaf had all been taken out by precision-guided bombs.

“So he’s toast, you think?” Bill O’Reilly on Fox News asked about Sahaf. “That’s what I’m told,” said Coughlin. As we now know, Con was told wrong. As many of us were. Human Rights Watch has since blamed the stupid use of smart bombs, as blunt instruments of assassination, for killing many of the innocent civilians who died during Operation Iraqi Freedom. It appears they killed few or none of the targets they were supposed to hit.

One incident was worse than the others, however, because it turned the course of the long-term war against us. On April 11, two days after American Marines pulled down the statue of Saddam in the middle of Baghdad, the United States tried to kill Saddam’s half-brother, Barzan al-Tikriti, by dropping six J-Dam guided bombs on a large villa about 11 miles outside of the city of Ramadi.

They didn’t get Barzan, if he was ever there, but they did kill Malik Al-Kharbit, a tribal leader who had worked with the Americans and Jordanians since the mid-1990s to try to overthrow Saddam Hussein. In addition to Malik, another 21 members of his family died under those bombs, including a dozen children.

War is war, with all its collateral implications. But some actions in war are more foolish and self defeating than others. Members of the Kharbit clan are considered the leading figures in an extended tribe called the Dulaym, who number as many as two million. Their strongholds are in Fallujah, Ramadi, Ka’em, Rutbah–places now well known to the U.S. public as “The Sunni Triangle,” where so many Americans have gone to die since that precision strike on the wrong target in April 2003.

How do you fix a screw-up like the killing of Malik Kharbit and his family? The Americans never did figure that out. In fact, they’ve made things worse. A few weeks ago, after Malik’s brother Mudher refused once again to cooperate with the United States and rein in the insurgents, eight members of his family were thrown into Abu Ghraib prison, including one brother who’d lost all his children in the April 2003 bombing.

“We are looking to the future,” Mudher told me when I saw him in Jordan over the weekend. He doesn’t trust Allawi. But he doesn’t want to fight the central government forever. He’d like to work with it, have his tribe have a place in it. If Allawi can find a way to accommodate the Kharbit clan, then once again he may be moving his country from war toward peace. An amnesty for those who’ve killed Americans is one way to start.

Of course, when you think of all the blood and money we’ve spent here, all this could seem pretty demoralizing. But given the mess we’ve made of this place, it’s surprising how reassuring it is to see the Iraqis reverting to their old ways.