What should President Obama do to build on what is widely acknowledged to be Iraq's fragile peace?

As Obama has frequently observed, the United States needs to be "as careful getting out of Iraq as it was careless getting in" because, unlike the case of Vietnam, the United States has substantial strategic interests in Iraq.

The country sits on the world's second largest oil reserves, is close to Israel, plays a lynchpin role in regional stability in a part of the world that sets global energy prices, and its reversion into a failed state would be a prelude to al Qaeda regrouping there.

The Iraqi economy is in tatters, though there are substantial improvements in oil revenues. The main economic issue is jobs, jobs, jobs and without them young men will drift back into the militias.

To help jumpstart the economy, Obama must engage with the Gulf states to provide investment and/or partner financially with American reconstruction efforts. There are already some baby steps in this direction with Bahrain and the United Arab Emirates naming ambassadors to Iraq, and this trend needs to accelerate.

The most critical political issue that remains unresolved is the status of Kirkuk, the capital of the northern oil industry and a city that the Kurds regard as a rightful part of Kurdistan.

Whatever the rights or wrongs of the issue, Iraqi Arabs universally do not want the oil-rich city to secede, and Turkey has made it clear that if it does do so it would lead to war with the Kurds.

The Obama administration should tell the Kurds to back off on the Kirkuk issue as it threatens to engulf Iraq in another civil war.

The Kurds have de facto enjoyed their own relatively prosperous and free state since 1991 under an American security umbrella and in the recent budget law garnered 17 percent of the Iraqi budget. Almost all of it came from oil revenue, which is a fair deal given the fact they make up just under a fifth of the Iraqi population.

Obama's team should quietly tell the Kurds that that they have as good a deal as they are ever going to get, which they would only endanger with their fantasy of bringing Kirkuk into a greater Kurdistan.

Another difficult issue that will likely face Obama is the prospect of a unilateral Israeli strike on Iran's nuclear facilities. It is widely understood that there is no way to take out all of those facilities. But Israel, which sees Iran's nuclear program as an existential threat, is prepared to do whatever is necessary to delay that program as Iran comes closer to acquiring nuclear weapons, which seems almost certain to happen over the next four years.

Such a strike would immensely complicate U.S. efforts in both Iraq and Afghanistan as the Iranians would presume that there was an American green light for the attack and would unleash its paramilitary Qods Force against U.S. targets in both countries.

The Obama administration should tell the Israeli government that there are no circumstances in which it will sanction such a strike.

Obama had promised to withdraw all U.S. soldiers from Iraq by 2010, although he has said he would retain a "residual force" to perform missions such as counterterrorism against al Qaeda in Iraq (AQI) and force protection for U.S. facilities such as the new U.S. Embassy in Baghdad, the largest American diplomatic post in the world.

During the campaign, Obama avoided saying exactly how large that residual force would be, as to do so in any detail would likely have alienated his anti-war base.

How large should the residual force be? According to senior military commanders I have spoken with, the minimal recommendation for a viable U.S. military presence in Iraq capable of defending itself will be at least four to five combat brigades and possibly as many as eight.

They will need to be supported by "enablers" who perform other functions such as intelligence, medical and aviation support. The recommendation that Obama will hear from his commanders is likely then to fall in the range of 30,000 to 60,000 soldiers to stay in Iraq beyond 2010.

Those soldiers will have to be withdrawn by the end of 2011, according to the terms of the present status of forces agreement between the United States and Iraq that was ratified by the Iraqi parliament on November 27, 2008. (Although it seems likely that a much smaller deployment of advisers and Special Forces would likely stay in Iraq after that, whatever the terms of the present status of force agreement.)

The Obama administration will face other predictable challenges going forward in Iraq that are not problems on the scale of Kirkuk, but any one of which can help to reverse the fragile peace.

The Iraqi government will only take 20 percent of the 100,000 Sons of Iraq (SOI) into the army or police, as it doesn't want to upset the ethnic equilibrium of those forces. What to do with the other 80,000 mostly Sunni SOIs is a conundrum as they are all in the process of being moved off of the American payroll. Many could drift back into the insurgency.

Another wild card is the issue of refugee returns. There is virtually no planning by either the American or Iraqi governments for the resettlement of millions of Iraqis who may return to their homes in Iraq as the violence recedes. Most of the refugees are Sunni and many would return to houses occupied by Shia families.

There might be some important lessons learned from the experience of the some 5 million refugees who have returned home to Afghanistan since 2002, an orderly return that has been largely managed by the United Nations.

And al Qaeda in Iraq could regain an important role in the country, despite its much-weakened state today.

With the death of Abu Musab al Zarqawi in 2006, AQI no longer has a charismatic leader. The foreign fighter flow into Iraq has declined from around 120 a month to about 20 a month.

This is a key to peace as about half of these foreign fighters are volunteers for suicide missions. As a result AQI has defaulted to increasingly using women as suicide attackers. Needless to say this has done little for its poor image in Iraq.

Operations against AQI this past summer around Mosul in the north of Iraq were supposed to finally put the kibosh on the group, but it has proven surprisingly resilient. Intelligence officials are worried that AQI could play the nationalist card quite effectively in the north, especially over the Kirkuk issue. After all, despite its largely foreign leadership, AQI is made up mostly of Iraqis.