Is winning in Tikrit really the key for Iraq retaking Mosul?

It can't hurt. But Iraq reasserting control over its territory is going to prove a lot more complicated than that.

The battle for Tikrit - a Tigris River town about 80 miles north of Baghdad - has been presented by Iraqi officers and their supporters as a spring-board for a successful assault on Mosul, the northern Iraqi city that the Islamic State seized last June.

Claims made last week that Tikrit, the hometown of former Iraqi dictator Saddam Hussein, was back in government hands have proved premature. Reuters reports that the Iraqi soldiers and Shiite militias fighting for control of the town have been stalled by the difficulties of urban combat and the improvised explosive devices and booby-traps that the Islamic State has laid in the town.

But if and when the battle for Tikrit is over, it may well contain more warnings than lessons for the much more difficult fight ahead in Mosul. Tikrit is about a third of the size of Mosul, and is 140 miles closer to Baghdad and the country's Shiite Arab dominated south. Maintaining supply routes that much further north will be harder and more dangerous, and IS fighters have held Mosul since last June, giving them over 8 months to prepare their defense.

And the character of the force coming to take back Mosul will give many of the Sunni Arab residents of the town pause. The stunning success of the Islamic State in Mosul was made possible by the behavior of the Shiite-dominated Iraqi army in the town, which treated its residents as vanquished enemies more than fellow Iraqis, and engaged in a range of protection rackets and theft preying on the local population.

Local anger at the sectarian nature of the Iraqi army in the area made the Islamic State's job a lot easier, as did the weak leadership and low morale of the troops stationed there, which saw Iraq's forces flee the city without putting up much of a fight.

Now a largely Shiite-dominated force is once again coming to "liberate" the city's residents. While the Shiite militias that will probably be in the vanguard, as they are in Tikrit, have more will to fight than the regular Iraqi army, many Sunni Arabs view them as death squads in waiting who will likely seek revenge on the city's population.

It hasn't helped that Gen. Qassem Soleimani, from the Iranian Revolutionary Guards, has been repeatedly  spotted directing operations in Tikrit, frequently surrounded by US-supplied weaponry. Former Iraqi Prime Minister Nouri al-Maliki, whose highly sectarian government sought to purge Sunni Arabs from Iraqi public life, has also visited with the militias on the outskirts of Tikrit.

While there do not appear to have been many reprisal killings so far, many of the Shiite militias working with Iran in the Tikrit area participated in the sectarian massacres during the US occupation of Iraq that reshaped the demographics of Baghdad and many other towns. Executions and torture were widespread on both sides.

Neither Iraq's militias nor its regular forces have cleaned up their acts in the years since. And Iraqi social media has been flooded with images of atrocities allegedly carried out by government forces, as ABC noted last week:

US-trained and armed Iraqi military units, the key to the American strategy against ISIS, are under investigation for committing some of the same atrocities as the terror group, American and Iraqi officials told ABC News. Some Iraqi units have already been cut off from US assistance over "credible" human rights violations, according to a senior military official on the Pentagon's Joint Staff.

The investigation, being conducted by the Iraqi government, was launched after officials were confronted with numerous allegations of “war crimes,” based in part on dozens of ghastly videos and still photos that appear to show uniformed soldiers from some of Iraq's most elite units and militia members massacring civilians, torturing and executing prisoners, and displaying severed heads.

The regular Iraqi army's behavior is, if anything, restrained to the Shiite militias now leading the fight. Gen. Martin Dempsey, chairman of the joint chiefs of staff, told the Senate Foreign Relations Committee last week that Shiite militias fighting for Tikrit number about 20,000, far more than the roughly 3,000 regular Iraqi army soldiers working with them.

"There's no doubt that the combination of the Iraqi Security Forces and the Popular Mobilization Forces are going to run ISIL out of Tikrit. The question is what comes after in terms of their willingness to let Sunni families move back into their neighborhoods -- whether they work to restore the basic services or whether it results in atrocities and retribution," Dempsey said. "The activity of the Iranians and their support for the Iraqi Security Forces is a positive thing in military terms against ISIL – but we are all concerned about what happens after the drums stops beating, ISIL is defeated, and whether the government of Iraq will remain on a path to provide an inclusive government for all of the various groups. We're very concerned about that."

ISIL is the US government's preferred acronym for the Islamic State. Dempsey's comment on an "inclusive government" for Iraq has been a central US talking point on the war. The complete failure of national reconciliation since Saddam Hussein was overthrown in 2003, which saw Iraq's long-repressed Shiite Arab majority come to dominate the nation's politics, is a key reason so many Sunni-Arab majority areas like Tikrit and Mosul have fallen outside of Baghdad's control.

But there's been little in the way of genuine signs that Iraq's Shiite leaders, including Prime Minister Haider al-Abadi, who replaced Mr. Maliki last August, are interested in an inclusive government. Iran, which has been crucial to the fight-back against IS, is certainly not interested in that. The Sunni-dominated regime of Mr. Hussein was the Islamic Republic's most important regional enemy, and his removal saw an Iranian-friendly Shiite government installed in his stead.

Anything that threatens that state of affairs would be viewed as a strategic catastrophe in Tehran.

The US effort that helped calm the worst of Iraq's civil war by 2009 was built around the notion that gains wouldn't be lasting if Sunni Arab's weren't given a better deal in the new Iraq. Promises were made by the US and Iraqi government to Sunni tribesmen, who joined the fight against the Islamic State's predecessor, Al Qaeda in Iraq (AQI), that jobs and government posts would be distributed to them. The Shiite-dominated government reneged on those promises, setting the stage for the Islamic State, which has achieved what AQI only dreamed of.

Now, the US is betting on reconciliation again - in a climate where it has far less influence than it did when Gen. David Petraeus was commanding US forces in the country. The country's Sunni-majority tribes have not forgotten that betrayal. And the country's Shiite militias don't seem interested in American political tutelage.

Yesterday Hadi al-Amiri, the leader of the Badr Corps, a militia closely-linked to one of Iraq's largest Shiite political parties, lashed out at the US. He praised Iran's "unconditional" assistance to the war, criticized the US as a duplicitous ally, and scornfully dismissed Iraqi leaders who "kiss the hands of the Americans and get nothing in return."

Most of the residents of Mosul aren't happy being ruled over by IS, with its love of public executions and floggings for crimes like smoking cigarettes. But when the Shiite militias finally turn towards Mosul, they also have much to fear.