It was the dead of night when Iraqi commandos advanced into the neighborhood deep in eastern Mosul.

Dozens of the black-clad soldiers waded across a small river that separated them from Islamic State positions. Night vision goggles cast the terrain in front of them in a green glow. 

On the other side, they fought house to house, helping the engineering teams make space for the main attack force. The Humvees then rolled through.   

The surprise nighttime attack in the Muthanna neighborhood earlier this month is among the adjustments Iraqi forces are making to jump-start their fight to take the northern city of Mosul. It was the first night operation in their fight against the Islamic State. 

In recent weeks, the number of advisers from the U.S.-led coalition assisting them has also increased, and airstrikes used to disrupt deadly car bombs have intensified.

Although Islamic State snipers took potshots at passing Humvees a day after Muthanna was retaken, the battle here was largely over in a matter of hours. Iraqi forces also have quickly advanced in other neighborhoods nearby, seizing the university and key government buildings and reaching the Tigris River, which carves the city in two. 

“They fled,” a 50-year-old teacher, who was staying at a relative’s house that is now on the front line in Muthanna, said of the militants. “It’s like we were buried and now we can breathe again.” 

It’s a shift in tempo in what had become an exhausting street-to-street battle in the militants’ last major stronghold in the country. Iraqi forces say they now control more than 80 percent of the eastern side of Mosul, and bridges to the west have been bombed, making it difficult for the militants to move in reinforcements.

But after three years of relentless fighting against the Islamic State, the beleaguered Iraqi troops will soon have a whole new battle to wage. On the other side of the Tigris is western Mosul, home to the city’s main government buildings — and even more densely packed with civilians. 

In the first months after the offensive began this past fall, Iraqi troops suffered heavy losses, largely from car bombs, the Islamic State’s most ferocious weapon. The Iraqi government does not release casualty figures. But the casualty rate for elite Iraqi counterterrorism units doing the bulk of the fighting had reached about 20 to 25 percent, according to a general, who spoke on the condition of anonymity because of the sensitivity of the subject.

The rate has dropped since the Iraqi government restarted the offensive in late December after a pause during which forces were reorganized, said Brig. Gen. Yahya Rasoul, spokesman for Iraq’s Joint Operations Command. “We are using new tactics and strategies, and we have reduced the casualties during the second phase.”

He said the losses among Iraqi forces are insignificant compared with Islamic State deaths in the battle. Iraqi commanders say at least 2,500 militants have been killed. 

Since the operation has restarted, the U.S.-led coalition has “significantly intensified” what are known as “terrain denial strikes,” said Col. John Dorrian, a coalition spokesman. Such strikes leave craters in roads that slow down or stop would-be car bombers trying to attack Iraqi forces. 

Iraqi army and federal police forces also have made greater inroads into the city, opening multiple fronts against the militants and relieving pressure on the elite counterterrorism troops. Some military analysts say that pressing so far into the city before it was completely isolated was a miscalculation.

“The counterterrorism units shouldn’t have started in the east until the other axes had arrived,” said David M. Witty, a retired U.S. Army Special Forces colonel and former adviser to the Iraqi counterterrorism force. “It was a mistake. [The Islamic State] was able to focus all its fighters on them. These are soldiers that can’t easily be replaced.”

The counterterrorism forces have been reinforced with about 300 new soldiers, according to Lt. Gen. Abdul Ghani al-Asadi. They also have received about 70 new Humvees, and a graveyard of wrecked vehicles on the road into Mosul has been cleared. About 40 new advisers from the U.S.-led coalition are assisting in and around Mosul, Dorrian said. 

Some of them can be seen with Iraqi forces deep inside the city. Coalition advisers are embedded with federal police forces as well as Iraqi army and counterterrorism troops. The “secret sauce” for the increased momentum has been the coordination among those three axes of advance, Dorrian said. 

“Daesh has no answer for this because it gives them more problems to solve than they can handle,” he said, using the Arabic acronym for the Islamic State.

But the militants are also making adjustments. Car bombs have become less frequent, although those that are used are now largely in civilian vehicles rather than fearsome steel-plated trucks, making them less effective but harder to spot. The militants are also using armed drones more often, soldiers say. 

The crack of machine-gun fire filled the air as several Islamic State drones buzzed over a convoy carrying Iraqi generals to survey the front lines in Muthanna. Two were shot down, but not before they dropped their explosive payloads, which missed their mark. 

“The tactics, techniques and procedures that Daesh uses every day continue to evolve,” said Maj. Gen. Joseph Martin, head of ground forces for the U.S.-led coalition. “They are very agile.” 

However, he said he is impressed with how the Iraqi forces have also continued to adapt to counter them and win back ground — nearly 12,000 square miles since 2014. 

Commanders expect to recapture all of eastern Mosul in the coming weeks, but no one knows exactly what will await them in the west.

There are about 750,000 civilians in the western side of the city, compared with 500,000 in the east, Rasoul said. The narrow streets of the old city could make for a more challenging environment, and it is unclear how many fighters the Islamic State has kept in reserve there. 

“I think they pushed most of their fighters and car bombs from the west to the east,” Rasoul said. “Despite all that, they still have the ability to strike, but as a force they are collapsing.”

The militants appear determined to drag out the fight as long as they can. 

“They are certainly going to fail to finish this battle in a short time,” read an article in an issue of the Islamic State’s al-Nabaa newspaper published shortly before the offensive began, found in one of the group’s training camps in Mosul. “This is not a battle of one or two days, or one or two months.” 

“Each day is going to cost them tens of millions of dollars,” it said. “Maintain pressure on them. Exhaust, by God’s will, all of their capabilities.” 

In the house on the front lines, the teacher was too afraid to give her name in case Islamic State militants returned.

“Please don’t let them come back,” she pleaded to an Iraqi soldier. “We are so afraid because they are very strong.”