Life in Iraq is getting better. Take one example: two or three years ago, tattoo artists in Baghdad were working overtime giving distinctive tattoos to men who feared they would be killed in the Sunni-Shia sectarian slaughter.

Aware that the faces of so many who died were being mutilated, potential victims wanted their families to be able to identify their bodies through a special mark known only to close relatives. One man had an olive tree tattooed on to his body because his father had planted one on the day he was born.

This grisly ritual is no longer taking place because Iraq is now a safer place than it was at the height of the sectarian bloodbath in 2005-7, when 3,000 bodies a month were being stacked up in the morgues. Tattooists report that their clients are today seeking to be marked with the image of a falcon, tiger or dragon for solely decorative reasons.

The point is that security in Iraq is improving, but from a very low base. Baghdad is safer than it used to be though this still leaves it as one of the most dangerous cities in the world, certainly worse than Kabul, with perhaps only Mogadishu in Somalia edging it into second place.

Iraq still suffers from horrendous levels of violence and this has never really abated, despite propaganda lauding the achievements of the American military "surge" which supposedly brought peace to much of the country. The media, both foreign and domestic, was suddenly full of feel-good stories such as the beginning of the return of five million refugees to their homes, though in practice few have come back.

By over-selling the extent to which Iraq had returned to peace since 2007, the Iraqi and American governments have left themselves open to the perception that an upsurge in bombing over the past month means the country is returning to war. The Iraqi Interior Ministry says 450 civilians were killed in June, double the figure for the previous month, and a further 566 civilians died in July after US troops pulled out of Iraqi cities on 1 June.

On returning from Iraq, people used to ask me hopefully if "things are getting better there" post-surge. I would routinely explain that "better" Baghdad might be, but it was still pretty bad. A more common query these days concerns whether or not "security is disintegrating now that the Americans have left the cities". There have certainly been more devastating bomb explosions and more people are being killed or injured. But the Americans were never able to stop this at the height of their strength in Iraq.

Regardless of who handles security, it is impossible to stop trucks packed with explosives or individual suicide bombers blowing up in market places, shrines, mosques or bus stations where they will cause maximum civilian casualties.

The targets are almost invariably Iraq's Shia majority and the aim is to provoke the Shia into retaliation against the Sunni minority, who then might return to supporting al-Qa'ida in Iraq, or look for backing from a foreign state. So far the Iraqi Shia have not risen to the bait.

The spectacular recent bombings divert attention away from the fact that the two wars which convulsed Iraq after the overthrow of Saddam Hussein by the US military in 2003 are largely over. The first was by the Sunni Arabs (20 per cent of the population) against the American occupation and was waged from 2003 to about half-way through 2007.

It was effectively ended by the outcome of a second conflict, this time an extraordinarily bloody civil war between Sunni and Shia (60 per cent of the population). It was the Shia victory in this war, fought primarily in Baghdad and central Iraq, which forced the Sunni insurgents to end their guerrilla struggle against the Americans.

Neither war looks likely to reignite or return to its former level of violence. The American forces are going. Their combat forces will be out of Iraq in a year's time. All troops will be gone by the end of 2011.

The Iraqi government is strictly interpreting the Status of Forces Agreement signed by the US and Iraq last year so that it limits and controls American military actions. Some US officers have suggested withdrawing earlier than planned, rather than see their troops confined to bases as if they were prisoners.

The American military withdrawal stabilises Iraq to a degree never admitted by protagonists of the original invasion. Foreign occupation deepened sectarian and ethnic hatreds because the three main Iraqi communities took radically different attitudes towards it. The Kurds supported it (though Kurdistan was not occupied), the Sunni fought it, and the Shia co-operated with it, just so long as they needed to do so to take power through winning elections and forming a government.

The American occupation destabilised Iraq in a second way because it frightened Iraq's neighbours. This is scarcely surprising since the neo-cons in Washington openly sought regime change in Tehran and Damascus, as well as Baghdad. So long as an American land army was in Iraq, they were always going to foster Sunni and Shia guerrilla groups attacking US troops.

As the Americans depart, there are several dangers for Iraq. One is that the Sunni states will refuse to accept the first Shia-dominated government in the Arab world since Saladin overthrew the Fatimids, and that they will support Sunni resistance to it. The second danger is that the victors, in this case the Arabs and Kurds who make up the present coalition government in Baghdad, will fall out and come to blows.

The Iraqi Kurds' quarrel with Prime Minister Nouri al-Maliki is over control of the disputed territories, including Kirkuk, captured by the Kurds in 2003. Separate armed forces, loyal to Baghdad and the Kurds respectively, are seeking to dominate this no-man's land. Each side is making serious threats, but both may ultimately pull their punches because they have so much to lose in a real war in which neither could win a decisive victory.