As she surveyed the view from the slopes of this strategic peak near the Syrian border last week, a young Kurdish fighter was optimistic.
Beyond the grazing sheep and tents of those displaced from the city of Sinjar below, she could see the road leading out of town toward the Syrian border — quiet for now, though still plagued by Islamic State snipers fighting Kurdish forces street by street.
"It's the main life-giving vein for ISIS in Mosul," Navita Aryen, 23, said of the road, which runs about 50 miles east to Mosul, Iraq's second-largest city, now controlled by the extremists. "Once we cut them off, we can then move on to other areas."
But with Islamic State shifting resources to Sinjar and to Tall Afar, a mixed Sunni-Shiite city on the road to Mosul that has a military airport and a population of 200,000, others questioned how soon the area could truly be secured.
The strategic battle for control of the Sinjar supply routes began last summer, after Islamic State seized Mosul, a city of more than a million, and laid waste to surrounding villages — capturing, enslaving and killing members of the Yazidi religious minority.
More than 10,000 Yazidis fled in August into the Sinjar mountains, where they became trapped; President Obama cited their plight when he initiated an airstrike campaign against Islamic State in September.
With that backing, Iraqi Kurdish forces, including the fighters known as peshmerga, launched an offensive from Mt. Sinjar last month that leader Massoud Barzani said routed Islamic State from the area.
"We have opened and controlled all the roads and broken the siege imposed on Sinjar Mountain," Barzani said during a visit to the area on Dec. 21. "We will crush Islamic State."
In the days that followed, peshmerga commanders insisted that they would retake Sinjar city, cutting off Islamic State supply routes to Mosul, which had been facing shortages of food, fuel, water and other staples. They secured numerous towns, as well as the Rabia border crossing into Syria, but have yet to retake Sinjar or Tall Afar.
Sinjar was once a city of 88,000, but is now a ghost town of burned and bombed buildings, Kurdish commanders said.
At a peshmerga command post on Mt. Sinjar last week, Kurdish official Saeed Shingali said Islamic State fighters had been weakened by recent airstrikes, which destroyed their heavy armor and lowered morale.
"They've shifted to a defensive stance," he said as peshmerga fighters loaded up trucks nearby and prepared to descend the mountain to continue fighting.
Peshmerga commander Said Qasim arrived, automatic rifle in hand, and said that as his forces tightened their hold on the area in recent days, the insurgents' supplies have dwindled. With fewer reinforcements, he said, the fighters have become desperate.
"There is weakness. The roads are still open from Tall Afar so they are still getting supplies, but we've heard them on their walkie-talkies calling for supplies, saying they only have four mortars left," he said. But, he added, "unless we cut them off from the border, there's no way to secure the area."
The towns and villages along the border here are a wasteland of bombed buildings, rubble-strewn streets and fields where red flags mark roadside bombs.
In the village of Sinoni, an abandoned Islamic State tank sat on a corner near where Jengana Akbar, a fighter with a Kurdish flag tied around his head, said he recently found a Yazidi man's decapitated body dumped by Islamic State fighters.
Local businesses still bore Islamic State fighters' graffiti, including, "The lions of God," "Islam or death" and "The Islamic State remains — and it's expanding."
Mayor Nayef Qasim was back in his spare office last week behind broken windows, trying to get his town and 45 surrounding hamlets, once home to 148,000 people, running again.
Qasim, who is Yazidi, said Kurdish fighters could retake Mosul, but must first block Syrian shipments, forcing Islamic State to detour south through Anbar province, much tougher terrain.
"The road to Anbar is desert, harsh desert," Qasim said. "But the border here is easy to cross."
In order for Kurdish fighters to split Islamic State and win control of the border region, they need more airstrikes and a better-equipped army, he said.
"Without intense airstrikes to pave the way, these forces can't go in" to Sinjar and eventually Mosul, he said.
Maj. Neysa N. Williams, a U.S. military spokeswoman, said decisions about airstrikes had to be coordinated with the Iraqi military. She deflected a question about the strategic significance of securing the Sinjar area, saying, "Our goal is for the Iraqi security forces to stand on their own but not stand alone, and ensure that Iraq is able to defend its borders and prevent another group like [Islamic State] from happening."
Dozens of Sinjar families remained camped on the mountain last week in blue-and-white United Nations refugee tents, unable or unwilling to return to their homes, which might be booby-trapped, on roads that Islamic State fighters had laced with land mines.
"We're waiting for the battles to finish so we can go back. No one has gone back to the city itself. You still have mortars, snipers, IEDs," said Ghazi Khalaf, 36, a father of eight who fled Sinjar in August.
As peshmerga fighters strategized nearby, Khalaf and his relatives sat on mats next to a rock overlooking their hometown.
Khalaf, a former border policeman, was not optimistic that Kurdish forces will be able to secure such a large swath of territory. Neither were the others.
"Even if they take back the areas, it's too large a border to police," said his brother Faisal Khalaf, 38, a vegetable vendor.
They worried that peshmerga commanders will claim Sinjar is secure and shift elsewhere, leaving them at the mercy of Islamic State, who could reemerge and recapture the area.
"When the commanders leave, what do you think we're going to do?" the former policeman said, staring down the mountain to where the fighting continued.
Bulos is a special correspondent.