It is the last day of my month in Baghdad and one of the Times drivers is bringing his children to meet me in my hotel. Nowhere else in the world would that be noteworthy, but in Iraq it is remarkable.

I had not seen his family since November 2003, a few months after the US invasion, when I visited their house in western Baghdad. Shortly after that, Iraq began its slide into mayhem. Westerners faced kidnapping and execution. Our driver and his family were forced from their home by sectarian death threats. They returned when the US troop “surge” finally restored a modicum of order last summer, but even then the children were locked inside the house.

As I await their arrival, I reflect that in five years of visiting Iraq this is the first time I have left feeling anything but deeply pessimistic. Even ardent opponents of the US invasion - myself included - could not deny that daily life for most Iraqis is now better, or at least markedly less awful, than it was.

There is less gunfire, and fewer explosions. No longer do I instinctively look for mutilated torsos floating down the Tigris. I have ventured out to shop and eat - albeit in one of Baghdad's safest districts. The night-time curfew has been relaxed. Schools, markets and the national theatre have reopened. Families visit refurbished parks. Men sit outside cafés drinking sweet, black tea. Children play soccer on side roads.

I found myself writing less about death than rising oil exports, the opening of Baghdad's first Chinese restaurant, and the resumption of a rudimentary passenger train service to Basra. It has been a welcome change.

American soldiers are increasingly focused on encouraging reconstruction, not preventing destruction, and for the first time I sensed that they felt good about their mission. The Iraqi security services - particularly the army - are gradually expanding and improving. Moqtada al-Sadr, the volatile Shia cleric, has just extended the six-month ceasefire of his infamous Mahdi Army militia that was responsible for so much sectarian killing. The threat of civil war has receded, and talk of Iraq breaking up has, for now, died away. The centre has held - just.

But all this must be set in context. What passes for normality in Iraq would be utterly abnormal anywhere else. The number of Iraqis killed in January was the lowest in 23 months, but still numbered 541. Hundreds of thousands of Baghdadis now live in walled-in, ethnically cleansed, heavily guarded enclaves that they are terrified to leave. Sunnis do not venture into Shia areas, and vice-versa. Sectarian hatreds have been contained, but not resolved.

The capital is choked by checkpoints and more than 100,000 sections of concrete blast barrier. Coils of razor wire roll across pavements like tumbleweed in Texas.

Some 50,000 exiles have returned from abroad since last autumn, but several thousand were so horrified by what they found that they left again. There are still four million displaced Iraqis.

Al-Qaeda, though on the defensive, is far from defeated. It still mounts spectacular attacks, notably last month's bombings of Baghdad's pet markets. Its killings of Sunni “traitors” - the concerned local citizens (CLCs) who switched allegiance to the Americans last year - have doubled since October. Headless bodies are found quite regularly in those provinces north of Baghdad where al-Qaeda is still a force.

The economy is forecast to grow 7 per cent this year, but mostly because of rising oil exports. Despite US efforts to nurture new Iraqi businesses, at least half the workforce lack proper jobs. Most of the rest work in the bloated public sector.

Iraq, blessed with the fertile, sun-soaked lands between the Tigris and Euphrates, used to be a net exporter of food. But agriculture has collapsed and the markets are now full of imported produce. The only foreign investment has been in the mobile telephone networks and three cement factories (building those blast walls is big business). Corruption is endemic.

To talk of America “winning” a conflict that has lasted longer than the First World War is now grotesque, whatever the outcome. There has been far too much suffering for that. This long ago became a salvage operation - and one whose success is still not assured.

Nouri al-Maliki's little-loved Shia-led Government has failed to secure the peace by creating more jobs or improving the country's abysmal public services, particularly water and electricity. It has not done nearly enough to promote reconciliation between Shias, Kurds and Sunnis. It has shown great reluctance to incorporate into its security services the 80,000 predominantly Sunni CLCs who have helped the US military to take on al-Qaeda.

Sunnis see the Government as a puppet of Iran, bent on domination, not reconciliation. Shias regard the CLCs as a fledgling Sunni militia, full of former al-Qaeda henchmen, whose alliance with the Americans is temporary and expedient. The Kurds are increasingly asserting their independence, signing bilateral contracts with Western oil companies, and a flashpoint looms in June with a referendum on the future status of the hotly contested, oil-rich city of Kirkuk, which the Kurds are determined to reclaim.

This is a dangerous state of affairs as the US troop surge starts winding down, but it is still hard to believe that anybody would want to return to the horrors of 2006 and 2007, or that a people who let the extremists lead them to the very brink of civil war would allow that to happen again.

I hope that is not naive, but it may be. Iraq's new-found “peace” is desperately fragile. My driver's family never made it to my hotel. Two car bombs exploded just down the road as they were nearing. They turned around and sped back home again.

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