After crosses were restored and flags raised in this Christian town near Mosul, elite units stayed behind for one of the least gratifying and most dangerous jobs in the war: the clean-up.

Constantly scanning their surroundings, five special forces members moved carefully down the streets of Bartalla, the muzzles of their rifles continuously shifting in every direction.

To provide cover, the gunners of four armoured vehicles in a convoy sprayed heavy fire around them as they moved slowly down two strips of asphalt.

"We're targeting suspect buildings and corners where we don't have good visibility," said Colonel Mustafa, adding that they also usually open fire on perpendicular streets in case snipers are lurking there.

These members of the counter-terrorism service (CTS) -- widely seen as Iraq's best fighting force -- are already first in line when Islamic State group jihadists have to be taken on in close combat.

But after a road, village or town has been secured and declared retaken, they criss-cross the area to sniff out snipers, enemies concealed in tunnels, car bombs and booby-traps.

"After liberating surrounding areas," a CTS officer who gave his name as Nabil told AFP in Bartalla, "we came back the other way to clean up the road."

This kind of mission is particularly dangerous because the bulk of their own force has already moved on to the next front and they have very little back-up.

Their protective gear is rudimentary and they disappear into tunnels wearing tee-shirts to hunt jihadists who might be hiding there.

Yet they are the cream of the crop of Iraq's armed forces. Their training and their salaries -- some cited a figure of around $2,000 a month -- are superior to most of the rest.

"They were trained by the Americans. They're really something else," Colonel Samer, who commands a tank unit in the regular army, said with a hint of admiration and envy in his voice.

The CTS is under the command of Prime Minister Haider al-Abadi, who in Iraq is the commander in chief of the armed forces.

Thanks to the United States, CTS also has better equipment than the average Iraqi soldier.

Anwar, who claims he was "the first to drive into the Bartalla battle", proudly displayed his night-vision goggles and pointed to the bullet impacts on his vehicle from that day.

To locate potential car bombs, those CTS units are also equipped with digital tablets they can use to enter coordinates sent to them by the US-led coalition.

- Coalition support -

"Their planes gather coordinates and send them to our commanders, who then pass them on to us. All we have to do then is to get to them with our vehicles," said Sergeant Amr, a radio to his ear and a tablet in his hand.

Next to him, the armoured vehicle's driver followed his instructions to support the men walking towards a building they wanted to inspect.

Above them, the gunner in his turret loads his ammunition.

"Left, right, turn and fire," Sergeant Amr said.

A barrage of gunfire was unleashed, several shots on every identified position, to check there was no return fire or explosion.

Sergeant Amr, a 27-year-old from Baghdad who joined the front line a month ago, just a day after his wedding, then briefly got out of his vehicle to confer with the unit moving on foot.

"We have EOD (explosive ordnance disposal) specialists -- they are the ones looking for IEDs (improvised explosive devices)," said Hamza, a CTS fighter wearing a scarf and an "Iraq special forces" cap.

"If they spot a car bomb, we come in to neutralise it," said the young man, who has already spent six years with CTS.

That is usually done by a controlled detonation.

"Job done! Mission over," Sergeant Amr finally exclaimed, putting down his radio.

Sitting on the pavement or the bonnets of their vehicles, the men scoffed rice rations before moving to the next target.

They still had around five kilometres (three miles) to cover before reaching the edge of the city of Mosul, as Iraqi fighters tighten the noose on the jihadist stronghold.