The Iraqi Army and Isis rebels are battling for control of Iraq's largest refinery outside Baiji, north of Baghdad, with each side holding part of the complex.
But in the town of Baiji itself, a few kilometres away, which is completely under Isis' control, residents say they are most frightened by the militants going door to door asking about the numbers of married and unmarried women in the house.
"They said many of their mujahideen [fighters] were unmarried and wanted a wife," said Abu Lahid. "They insisted on coming into my house to look at the women's ID cards [which in Iraq show marital status]."
Isis (the Islamic State of Iraq and al-Sham) says its men have been ordered not to bother local people if they are Sunni, but in many places they are imposing their puritanical social norms in captured towns.
In Mosul people were at first jubilant that Isis had removed checkpoints that for years had slowed movement in the city.
Merchants and farmers were told to reduce their prices. But tolerance and moderation on the part of Isis is intermittent and may be temporary.
In one case in Mosul, a woman was reportedly whipped with her husband because she was wearing a headscarf rather than the niqab cloak covering the whole body. In some captured towns militants started imposing rules about women's clothing, watching TV in coffee shops and cigarette smoking almost before the fighting ended.
The restraint, or lack of it, has important political implications. When al-Qaeda in Iraq, the forerunner of Isis, insisted on local women marrying their fighters during the Sunni-Shia civil war of 2004-08, they alienated much of the Sunni community. They killed even minor government employees.
Isis could isolate itself again through its brutality and bigotry, though its leaders show signs of recognising where they went wrong last time. Its fighters act as the shock troops of what has turned into a general Sunni uprising, but it is only one part, albeit the most important, of a loose alliance of seven or eight militant Sunni groups that could easily break apart.
For now, it is held together by a common sense of grievance and hatred of Prime Minister Nouri al-Maliki and his Government, which it sees as persecuting and marginalising the Sunni community. Maliki's departure will remove part of the glue holding together the Isis-led Sunni alliance.
Some strains between the Sunni rebel factions are already evident: when the Naqshabandi Army, of which Saddam Hussein's former deputy Izzat al-Douri is titular head, put up posters of Saddam in Mosul, Isis gave them 24 hours to take them down or face the consequences. They complied.
Government television channels try to push the idea that the Sunni coalition is already in disarray, but this is probably premature. In most Sunni towns captured by the insurgents, people say they are more frightened by the return of vengeful government forces than by the presence of Isis.
For the moment, the battle lines have steadied north of Baghdad after the blitzkrieg advance of Isis and its allies. The fighting for Baiji refinery has been swaying back and forth for five days. Further south, Isis holds Tikrit, though a resident said "many people are fleeing to Erbil and Sulaimaniyah in Kurdistan because they think that if the Iraqi Army returns, it will shoot everybody indiscriminately".
In Sunni areas Isis is still mopping up resistance: yesterday its fighters captured al-Qaim, close to the border with Syria, after a fight in which 30 government soldiers were killed.
One aspect of Isis' success receives too little attention. Its prestige has been enhanced across the Sunni world, especially among young men in neighbouring countries.
For a decade television in Sunni states has dwelt on the oppression of the Iraqi Sunni and it is undeniable that it was Isis forces that broke Baghdad's dominance over its Sunni minority. Isis successes may already be having an impact in Syria, where its fighters have overrun the headquarters of the Western-backed Free Syrian Army in Deir Ezzor province in the northeast.
In the mainly Shia city of Baghdad, there is terror of Isis breaking through and conducting a general massacre. It is noticeable that Isis has not activated its cells in Sunni enclaves and there have, by Baghdad standards, been few bombs. It may be that Isis is overstretched, but it could be waiting for its fighters advancing from the north to get closer to the capital before activating its cells inside the city.
Sunni and Shia in Baghdad are both worried for another reason. The Government has handed over security in many parts of the capital to militiamen who have been setting up their own checkpoints. Some belong to Asa'ib Ahl al-Haq, a splinter group from Shia cleric Moqtada al-Sadr's movements. It and Ketaeb Hezbollah, no relation to the Lebanese group, carry more authority than soldiers and the police, many of whom have melted away to stay home.
Baghdadis regard these militias as semi-criminal groups quite capable of kidnapping likely targets for ransom at their checkpoints. Asa'ib Ahl al-Haq is seen as under the influence of Maliki and the Iranians but its men generally act in their own interests.
The strength of the militias was on display yesterday in Sadr City. Twenty thousand armed men paraded with heavy weapons such as machine guns, rocket launchers and missiles. Sadr has pledged that these militia will act only in defence of the Shia shrines in Samarra, Baghdad, Karbala and Najaf, but the state's inability to defend these holy sites illustrates how far its authority has withered in the past fortnight.
The military situation remains fluid. "My bet is that the Government will not be able to retake Mosul, but Isis will not be able to keep it long-term," said an Iraqi political analyst who did not want to be named.
He argued that Mosul was traditional and nationalist and not particularly religious, so Isis would ultimately be evicted by its people.
Anti-Isis volunteers of the Peace Brigades rally in Sadr City. Photo / AP
That may be so, but Isis has proved by its ferocity that it is hard to dislodge. In its Syrian capital at Raqqa on the Euphrates it publicly crucified young men who had started an armed resistance movement.
Sunni insurgents led by Isis have expanded their offensive in a volatile western province of Iraq, capturing three strategic towns and the first border crossing with Syria to fall on the Iraqi side. The towns of Qaim, Rawah and Anah are the first territory seized in predominantly Sunni Anbar province, west of Baghdad, since fighters overran the city of Fallujah and parts of the provincial capital of Ramadi earlier this year. The capture of Rawah on the Euphrates River and the nearby town of Anah appeared to be part of march toward a key dam in the city of Haditha, the destruction of which would damage the electrical grid and cause major flooding. Iraqi military officials said more than 2000 troops were dispatched to the site to protect it.
Shia militia shows its muscle
For the past week the young and old of the Mehdi army had been preparing. New recruits, only children the last time the Shia militia all but ran Iraq, had been learning how to march and clean weapons.
Veterans of the insurgency against US forces and the civil war that followed had been signing up cadres. On Baghdad's streets, battered utes shuttled weapons from depots to mosques where the rapid rearming has transformed the already militarised capital into a war zone in waiting.
With the mobilisation complete, the now battle-ready militia presented itself to Iraqis once more, staging a series of parades that made an emphatic statement of its readiness and intentions.
One of the most feared names in Iraq was back in business, even if it was fighting under a different banner. This time around, the Mehdi army will be called the Peace Brigades, after its leader, Moqtada al-Sadr, decided a rebranding might shake it free from its infamous past.
Chanting battle hymns, they jogged past buildings still pockmarked by clashes with US forces who occupied the area in 2008 and had fought running battles with the Mehdi army for most of the nine years that they remained in Iraq.
Much of the vast, sprawling neighbourhood in Baghdad's northeast has been rebuilt since the Americans left. But it still gets bombed by a foe common to both, Isis.
Clashes here with US forces were such a centrepiece of the Iraq War that the prospect of the US Air Force now giving cover to the group in coming weeks seemed unfathomable for many of those on the sidelines of yesterday's parade.
"There is no way we can accept this," said Sayed Ibrahim al-Jabari, a senior representative of the Sadrist movement in Sadr City. "We have the military that can finish the job against Isis and we reject any foreign intervention."
But such is the perceived threat that many Mehdi army members are quietly hoping their former enemy tackles Isis sooner rather than later.
"Look, if the Americans want to go after [Isis] then let them," said one member, a police officer during breaks between wars.