A spine-chilling phrase has crept into the dictionary of life in Iraq -- "de-Ba'athification".

It means getting rid of the remnants of the supporters of the Ba'ath party's former Secretary General Saddam Hussein.

Many members of the party have fallen back into line, but justice is swift for those who don't.

I was out on patrol with the 60-strong Alma Company of the Duke of Wellington's regiment in downtown Basrah when we were suddenly called back, to get back into the heavily armoured Land Rovers.

The mission was to check the scene of a shooting somewhere near a mosque. It was a de-Ba'athification killing.

When we got there preparations for the funeral were already well underway and there was little or no involvement from the Iraqi Police Service.

I talked to witnesses who told me three men in a white Toyota car had pulled up. One masked man leapt out and shot the former Ba'ath party member three times.

The body was moved, the blood swilled away, and the funeral arrangements were underway all in the space of a couple of hours or so.

The children were trying to sell the bullet cases for one dollar each.

Incidents like that are getting more rare, but it is all part and parcel of a day's work for The Dukes.

My guide was Major Mark Robinson MBE, whose parents live in Grassington. Major Robinson was awarded the honour for "doing an intelligence job" in Op Telic 2 (the second part of the coalition action in Iraq).

The patrol's mission was to set up road blocks, randomly patrol streets and use a specially trained dog to search for explosives.

As we travelled from the Shatt al-Arab hotel base you could tell we were nearing the centre by the nose-wrinkling pungent smell. You need a fairly strong stomach for the job, which involves patrolling some streets which look to have come straight out of medieval times.

There's a carpet of filth and litter, often with an open sewer running down the street. It is hard to believe, but the scenes which greeted us are an improvement.

Major Robinson commented: "It may look like something out of Britain in the 1800s, but the fact is it is much tidier than Op Telic 1. Obviously there's still a lot of work to do."

On some of the main roads streets were being swept, and one incentive being offered in parts of Basrah is for residents to take rubbish to a massive dump, where it is burned.

Many of the ramshackle houses now have new satellite dishes -- which may look odd, but they are a tangible sign of freedom since the end of the Saddam regime.

The other signs of new-found affluence are mobile phones and cars. But they in turn present a threat to security.

Explained Major Robinson: "The number of attacks in the area is reducing, but the lethality of them is increasing. They are getting much better." Two of the favourite ways of detonating devices are to use the key pad of a mobile phone or the car key fob.

The insurgents -- many of them thought to be former Saddam anti-terrorist experts -- are getting more technically aware. Said Major Robinson: "They are like gamekeepers turned poachers."

As we strolled through the Al Fursi district, home to a large number of the minority Sunni community, the need for a cuppa called.

I stopped and chatted with some local Iraqis who were on guard duty outside an unknown aid agency building, having a brew before changing shifts. I shared a cup of sickly sweetened tea, being thanked by them for coming to see them.

I may only have met and chatted with less than a dozen of the 1.5million citizens of Basrah -- but to a person they were overpoweringly friendly. The welcome increased as soon as they realised I was British.

One resident, Gafal Dawood, said: "We all voted in the election. Now it is much better. I want us to have a good government working for everyone."

Added Major Robinson: "The first flush of enthusiasm after Op Telic 1 has died down. It has changed to one of seeing practical results. This is being done with the result that the insurgents are no longer getting the support of the local people."

He went on: "Around £4 million is being spent on a restructuring programme. It will take an awful long time to turn round 30 years of neglect."

The tour of the city took us back to the Five Mile Market, where everything and anything, ranging from police uniforms to nuts and bolts and live animals can be bought.

It was then time to making our way back to the Shatt al-Arab hotel. As we got back into the vehicles the interpreter took off his Hannibal Lecter style mask.

As a reminder of just how dangerous the country can be, he explained he was still in fear of being identified and facing the death sentence for working with the security forces.