Boys on bikes cycle backwards and forwards on a footbridge over a small canal lined with houses and groves of date palms. Women in headscarves look anxiously in groups from windows. Men walk with shopping bags. A gunman, clutching an AK-47, bobs his head around the corner of an alleyway close to a school.

Once. Twice. On the third occasion a child, a boy seven or eight years old, is thrust out in front of him. The gunman holds him firmly by the arm and steps out for instant into full view of the Bradley's gunner to get a proper look, then yanks the boy back and disappears.

"That is really dirty," says Specialist Chris Jankow, in the back of the Bradley, with a mixture of contempt, anger and frustration. "They know exactly what our rules of engagement are. They know we can't fire back."

A few minutes and a few hundred metres later the performance is repeated. A woman and three small children emerge uncertainly from behind a building, little more than a shack. They stare at the approaching armour. After a few seconds they retreat from view; then the process is repeated. The third time they emerge, a fighter is crouching behind them with a rocket-propelled grenade aimed at Jankow's Bradley. The group disappears.

There is a long pause, a moment of excruciating moral conflict for the soldiers and for the gunner in particular.

Not to shoot would be to imperil their own lives or those of their colleagues, both American and Iraqi. To shoot would be to risk killing civilians who have been shoved in front of their guns to shield insurgent fighters.

Suddenly, the decision is made, announced by the Bradley opening fire with four rounds from its 25mm gun, blasting a large hole in the corner of the building. Three bodies fall into view.

For a sickening few seconds it seems inconceivable that the woman and her children are not among the dead. A silence descends on the vehicle. But the bodies are those of men.

"This whole human shield thing is all fucked up," says Specialist Orlando Garcia, sitting in the Bradley's back. "You know, if I heard a Bradley. I would be under my house. I wouldn't be out here."

This is the horrible reality of a brutal and unconventional war in Iraq's north - where jihadi fighters use human shields and force children to run weapons for them.

The Iraqi army leading the fight appears to have been infiltrated by those it is fighting. In this "clearing" operation led by two battalions of the Iraqi army supported by a few squads of US troops, the fighters in Buhriz appear to have had ample warning.

The main route into the area - previously checked by unmanned drones - is now dotted with roadside bombs, one every 50 metres. A second route is only marginally safer, forcing the vehicles down to a crawling pace as they go in.

Minutes stretch to hours as the Iraqi soldiers, some 200 of them, search houses for weapons. There are small bursts of fire. An Iraqi Humvee is hit with an RPG, to little effect. Then, as the afternoon wears on, another Humvee in the column hits an improvised explosive device (IED) hidden by the road. The heavy vehicle is tossed on to its side, engulfed in an orange flame that reaches above the houses.

There is little chance that any of the four Iraqis inside can have survived, but one is pulled out of the burning vehicle and dragged across the road. He writhes for a while, and then is still.

The insurgents move among the residents, seen by the helicopters and drones above that report their movements to the troops on the ground. "Moving everywhere," the radio says. They appear on roofs as snipers, or as triggermen for the IEDs. They fire their heavy weapons across the little canal from among the date palm groves they know the armoured vehicles cannot cross, flickering figures manoeuvring expertly among the trees in groups.

It has been a "Darwinian process", an officer says afterwards. The stupid insurgents, and the ones who were too brave, are dead after three years of resistance. Those who are left are battle hardened and have adapted their tactics to fight most effectively against the US military.

As dusk falls with the column halted at the canal by yet another IED, and under fire from the date groves, an air strike is finally called in. The Gatling gun of an A-10 Warthog turns the tall trees into matchwood. With the darkness the column finally pulls out. Another day in a war that seems to have no end.