By Mark Urban
BBC News, Baghdad
As the search for three US soldiers abducted south of Baghdad continues, our correspondent - who spent three days embedded with US troops - says their comrades remain remarkably positive despite the dangers.
Down in the heart of Dura market there is an old cafe where American soldiers eat, smoke and chat.
It is a tiny space with five plastic tables, tiled walls and a sink that sometimes has running water.
It provides a social centre to the outpost where soldiers are trying to secure this part of Baghdad.
The first phase - blocking off the market so the stall holders could work in safety - was achieved earlier this year.
But the second, trying to extend that success to the neighbouring blocks, has brought tough opposition.
Sitting in the cafe late at night, we talked over the fight for Dura.
My BBC colleague, Mark McCauley, instructed Lieutenant Jake Carlisle in the art of rolling your own cigarettes. He also told him how it had felt, as a young Catholic from Londonderry in Northern Ireland, having British troops on the streets of his city.
US troops are trying to secure Baghdad
And I shared experiences from my time with Russian troops in Afghanistan.
All the time Lieutenant Carlisle and his platoon sergeant, Dorian Perez, drank up the experience and compared it with their own.
I had always thought of the US army as an organisation that did not exactly ban creative thinking, but severely limited it at lower levels.
And there were Lieutenant Carlisle and Sergeant Perez wondering how important waving and smiling were in Arab culture or considering the value of removing your sunglasses when speaking to Iraqis.
Sense of responsibility
Their platoon numbers 37, of whom two have been killed and several wounded since their operations started in Dura.
Shot at one hour and smiling at the locals the next, it would be the easiest thing in the world to get spiteful, Sergeant Perez told me, but it would also be totally self-defeating.
US troops operate in some of Iraq's most dangerous areas
The sergeant is 34 and he has been in the army for nearly half of his life.
I wondered how Iraq did not exhaust the positive energy or intellectual curiosity of a man like Dorian Perez.
You can marvel at the Americans' can-do spirit, as some British soldiers do.
You can see it in terms of America, the world's hyper power staring failure in the face and refusing to accept it.
But in the sergeant's case the will to carry on comes from a sense of responsibility towards the people of Iraq.
Sergeant Perez buys the so-called pottery shop analogy that seems singularly appropriate to the Dura market: if you break it, you own it.
The right balance
Lieutenant Carlisle is a 26-year-old from Wisconsin. He is a tall, lanky presence even in his body armour, loping down the dusty streets propelled by a young officer's enthusiasm or desire to do it right in front of his superiors, and, of course, us.
When I ask him whether they were right to storm one house, frightening the inhabitants, he does his best to back his men while conceding they probably should have done it differently.
In the end, he always has to explain the abrasive features of his patrolling in terms of the high threat they face from roadside bombs, snipers and the like.
And that balance between self-protection and alienating the local people is at the heart of many a late-night conversation in the cafe.
The British army
From the odd glimpse or overheard remark, I do not doubt that the second platoon contains the odd bad apple or loud-mouth, but as my time with them went on I became aware of an uncomfortable feeling.
When eventually I was able to identify it, I realised my unease concerned British soldiers, and how they compared with these Americans. Carlisle, Perez and the rest seem brighter, stronger and more committed.
The British army still has many outstanding qualities but it has had great difficulty recruiting for the past decade.
Many recruits who would once have been thrown out have been pushed through the training establishments.
In many British infantry battalions 15% or 20% are now Fijians or other Commonwealth contract soldiers.
The Americans, by contrast, may have had some recent problems staffing their army but they have been able to retain more of a sense of common purpose and drive.
If they are that good, you might ask, why are they not getting better results in Baghdad? There is history, of course, of terrible past mistakes.
There are numbers: Baghdad is a city of six million.
There is also ruthless intimidation by al-Qaeda of local people and the simple prejudice of those who will never like the Americans because they are unbelievers.
But there is no shortage of determination or creativity and tonight Sergeant Perez and Lieutenant Carlisle will probably resume their running discourse in the Dura cafe about how they can do it better tomorrow.