U.S. soldiers patrol in the city of Kirkuk. (SAAD SHALASH/REUTERS)

The talks are an important first step. But what American officials really want is clear: a decision.

This week, Adm. Mike Mullen became the latest American official to travel to Iraq push for answers on whether a U.S. presence is wanted after the formal withdrawal deadline passes. His calls came in the midst of an uptick of violence against American forces and the background noise of sectarian assassinations and bombings that never quite goes away. They also came as the Pentagon faces the challenge of trimming hundreds of billions of dollars from projected spending over the next decade.

But despite all the reasons to get out, American military officials have often sounded as though they would rather be invited to stay than given an excuse to leave. And, indeed, some defense analysts have said there are good reasons to maintain a presence, albeit reduced, in Iraq.

“We don’t need a large combat presence,” said Anthony Cordesman, of the Center for Strategic and International Studies. “We need Special Forces and perhaps some forces who would be effectively combat troops.”

To prevent hard-won security gains from slipping away, he said that American troops should continue to operate along the border with the semiautonomous Kurdish region in the north, where violence between Kurds and Arabs sometimes flares. He also suggested that an American training presence would help the Iraqis shore up their woeful external defense capabilities and encourage them to buy equipment from the United States, thus building up an American-Iraqi security relationship.

“It would be helpful,” added Cordesman, “for Iran to know that any action by them would trigger a response, an air response, from the U.S.”

Although he says that the reasons for staying are complex – “you can’t describe a game of chess as checkers” – it is clear that keeping a check on Iraq’s large and troublesome neighbor would be a significant factor in maintaining an American presence there. Iran is seen as retaining a strong influence over many of Iraq’s leading politicians, including Prime Minister Nouri al-Maliki. The Islamic Republic is engaged in a charm offensive in Iraq, opening consulates, investing in the economy and sponsoring religious scholarship, as well as less charming assertions of power.

The desire for a continued American presence as a counterweight to Iran is shared privately by some Iraqi lawmakers.

In order for some American troops to stay, Iraqi authorities would have to make a formal request to the United States. Ideally, this would happen through a parliamentary agreement, although Iraqi politics do not always adhere closely to procedure.

The broader question, in Iraq as in Washington, is how to sell it.

When American troops left Iraqi cities in 2009, people danced in the streets to celebrate. Maliki naturally sees Iraq’s sovereignty after so many years of strife as a point of pride. And the powerful political wing of the movement led by vehement anti-American cleric Moqtada al-Sadr would try to block anything that looked like a continued American presence — if only to maintain popularity with its power base.

The compromise over an enduring American presence may come from a semantic sleight-of-hand. Maliki may be able to persuade the government to accept American “instructors” on Iraqi soil.

That said, those calling on Iraq to make a decision may have a long wait. The government hardly has the greatest track record when it comes to making deadlines. Ramadan has started, the weather is scorching and the exasperation of American soldiers might prove no match for the obdurate inertia of Baghdad politics.