Don’t think for a moment that the United States isn’t still involved in Iraq. At the moment, the government of Iraq is preparing for what might be called the Third Battle of Falluja. That’s the city in Anbar Province, west of Baghdad, that was the scene of horrific clashes during the US occupation of Iraq in 2004. Now, Falluja is under the control of radical-right Sunni Islamists, Al Qaeda and elements allied with the Islamic State of Iraq and Syria (ISIS), and the government in Baghdad has been paralyzed in its efforts to retake the city.

Whatever happens, it’s going to be bloody once again. And although the United States withdrew its occupation forces in December 2011, the Obama administration has continued to view Iraq in the context of the regional competition with Iran, which has enormous influence with Prime Minister Nouri al-Maliki’s regime. Although Maliki, who lived in Iran during part of his exile in the Saddam Hussein era, is ideologically closer to Tehran than to Washington, he’s maintained political and military ties with the United States since 2011—including the supply of advanced US weapons—and it looks like the United States is trying to use the crisis over Falluja in 2014 to move Maliki closer to Washington and away from Iran. That’s a dangerous, zero-sum game to play.

First, some history. The First Battle of Falluja, in April 2004, was a revenge-minded US assault on the city after several American military contractors with Blackwater USA were killed and mutilated by an angry mob. But the battle was inconclusive, and to paper over its failure the United States withdrew in early May and handed control to something called the Falluja Brigade, a militantly Sunni, anti-Iran paramilitary force that was made up of some of the selfsame forces the United States was fighting when it went into the city. Then, in what would be called the Second Battle of Falluja, a massive, American-led force reinvaded the city in November 2004 and virtually destroyed it, causing thousands of casualties.

Now, Maliki—who’s ruled Iraq as a Shiite partisan, making bitter enemies of Sunni moderates, tribal elements and hard-core Islamists alike—is stuck. With the city once again controlled by Sunni Islamists who detest him, he initially considered a massive military assault on Falluja using his Shiite-controlled, Shiite-dominated Iraqi armed forces—but that, he probably knows, would provoke open civil war again. (Already Iraq is in the early stages of civil war, with nearly 10,000 killed in 2013 and another 900 dead in January in suicide and car bombings and other clashes.)

So the United States is urging Maliki to offer an olive branch to the Sunnis, to arm Sunni tribal elements, and to use the tribes in a neighborhood-by-neighborhood retaking of Fallujah. According to The New York Times, he’s aided not only by US arms but also by the support of 100 US troops still stationed in Baghdad at the US embassy, including Special Forces who are advising Maliki’s commanders. And the paper reports, General Lloyd J. Austin III, the commander of the US Central Command, met in Baghdad last week with the Iraqi military command. While the United States has an interest in suppressing Al Qaeda in Iraq, ISIS and its allies, it seems obvious that Washington would also like to use the crisis in Falluja to move Maliki away from his ties to Iran, which means reducing the power of the Shiites in Iraq and bringing the Sunni tribes back into the Iraqi political framework.

Certainly, it would be a good thing for Iraq if a healthier balance between Sunnis, Shiites and Kurds could be established in Baghdad. But it isn’t at all clear if Maliki understands what he has to do to begin the process of true political reconciliation. So it’s more likely that the Third Battle of Falluja will be more of the same: Maliki will use the tribes as a battering ram, retake the city and then fall back on his usual policy of keeping Iraq’s Sunnis at arm’s length and away from any real power. Which means that at some point there’s likely to be a Fourth Battle of Falluja, and other elsewhere.

In the meantime, members of Congress and Obama administration officials seem to agree that the United States needs to be involved more deeply in Iraq. Yesterday, Brett McGurk, the State Department’s top official for policy toward Iraq and Iran, told a committee of Congress that the United States is looking to get involved in training Iraqi forces “in Jordan or in the region.” In other words, Washington is hoping that Maliki is so desperate to solve the crisis in Falluja that he’ll turn to the United States for help. But make no mistake: the primary goal of the United States in Iraq—and in the civil war in Syria, too—is to undermine Iran’s regional influence. (Iraq, as has been widely reported, is allowing Iranian forces to overfly Iraq’s air space to aid its allies in the government of Syria’s Bashar al-Assad, and Iraqi Shiite militias have traveled to Syria to fight on Assad’s behalf—against the selfsame Sunni and Al Qaeda–linked rebels in Syria that are now occupying Falluja!)

Joining the fight in Iraq are “hundreds” of American contractors, according to The Wall Street Journal:

Hundreds of contractors working for America’s biggest defense companies are taking on a broader role in helping Iraq’s military learn to use new weapons in a growing battle against Islamist insurgents.… Across Iraq, military specialists are helping the Iraqi military maintain its growing number of surveillance drones, attack helicopters and powerful missiles. Thousands more support the U.S. government as security guards, analysts, drivers and cooks.…

Two dozen Lockheed employees are helping the Iraqi military keep their C-130 transport planes in the air. The company is also sending nearly 500 Hellfire missiles, which are being increasingly used in the fight against al Qaeda militants.

And more than a dozen employees with Beechcraft Corp. and General Atomics maintain a fleet of “Peace Dragon” surveillance airplanes used to track insurgent activity around the country.

According to the Journal, there are more than 5,000 American contractors in Iraq, and “those numbers don’t account for scores of military contractors working in Iraq as part of US-approved foreign military sales that provide the Iraqi government with helicopters, missiles and other critical support.”