BAGHDAD – The battle for Mosul has seen snipers, car bombs, missiles, oil-filled moats waiting for the torch, secret village-to-village tunnels, and a burning sulfur plant — and yet U.S. war leaders here warn that this is the light stuff. With each advance of Iraqi, Kurdish, and American forces, ISIS resistance is hardening.

In other words, things are going exactly as expected. Defense Secretary Ash Carter and U.S. Army Lt. Gen. Stephen Townsend, commanding general of coalition forces in Iraq, said they are pleased with how Iraqi, Kurdish, and American forces have positioned themselves in early fighting on Mosul’s outskirts. The anti-ISIS forces have squeezed an estimated 7,000 ISIS insurgents into their stronghold for a fight they predict will intensify with each kilometer.

“So far, it is proceeding according to our plan,” Carter said at Baghdad International Airport after a daylong visit with American commanders, Iraqi leaders, United Nations, and State Department officials in the city’s secure Green Zone. But there’s a feeling this week’s advances were all a setup for something much deadlier to come. “We’ve got tough fighting ahead,” he said.

One week into the announced start of the Mosul campaign, the top U.S. commander said progress for coalition forces has not been easier than anticipated, as some observers have argued.

“The resistance is about as we expected,” said Townsend, standing at Carter’s side. “It’s pretty significant. We’re talking enemy indirect fires, multiple IEDs, multiple vehicle-borne IEDs each day, even some anti-tank guided missiles. So, it’s been very tough fighting – snipers, machine guns. The Iraqis expected this and they’re fighting through it.”

U.S. military officials estimate about 1,000 to 2,000 ISIS fighters are positioned in Mosul’s outer bands, where 100 to 200 U.S. troops are in combat accompanying, advising, and assisting Iraqi-led coalition fighters. Already, the battle has claimed its first American military casualty in Navy Chief Petty Officer Jason Finan, who was killed after the Iraqi armored vehicle he was in struck an IED north of Mosul and rolled over. Finan died of his injuries later at the military base in Erbil. Footage on social media posted by reporters and Iraqi and Kurdish military feeds shows such blasts are increasingly common.

“It’s stiffened over the last couple of days, but that’s not really surprising,” Townsend said. “We see the enemy, they’re watching, and when an attack starts it takes them a couple of days to kind of figure out what we are up to. And they start voting.”

As Iraqi forces surround Mosul, U.S. officials again said the coalition will not attempt to close off escaping ISIS fighters to the west. “There’s not a plan to seal all the way around,” said another U.S. military official in Baghdad. “Thus far, we’ve seen no large movement either in or out of Mosul to the west.”

East of Mosul, Kurdish Peshmerga fighters already have reached their self-restraining limit on the eastern flank, clearing routes and villages up to roughly 20 kilometers outside of Mosul. They are nearing their boundary from the north, as well, according to U.S. military official in Baghdad who briefed reporters traveling with Carter. Per their agreement with Baghdad, the Peshmerga are expected to halt their advance, and then permit Iraqi police and army units advancing from the south to seize, clear, and hold Mosul.

In his meeting Saturday, Carter said he praised Iraqi Prime Minister Abadi for “the way this has been accomplished with Iraqi unity”— politician’s code for playing nice with the Kurds. Another common formulation is “the Peshmerga force have operated within the Iraqi Security Forces very successfully.”

Less unified is the uneasy way Turkey has inserted its forces into Iraq and the Mosul campaign without Iraqi permission. Carter in Ankara on Friday had said there appeared to be an initial agreement between the parties that Turkey should have a military role to play in the Mosul battle and counter-ISIS campaign beyond, and other non-military roles. But Abadi appeared to flatly reject the notion. After meeting Carter, Abadi said, according to a State Department translator, “That is important, for us to have good relations with Turkey. Turkey is a neighboring country but the Mosul battle is an Iraqi battle and the ones who are conducting it are Iraqis. I know that the Turks want to participate, we tell them thank you, this is something the Iraqis will handle and the Iraqis will liberate Mosul and the rest of the territories and thank God Iraqis and Kurds and Turkemans and Christians, they are all fighting together to liberate Mosul. We don't have any problems. If we needed help, we will ask for it from Turkey or from other regional countries.”

But first the coalition will need to get past layers of defenses ISIS has built over the past two years, including berms, booby-trapped houses, and trenches filled with oil the U.S. believes ISIS is waiting to ignite.

Yes, ISIS built a flaming moat.

It’s likely to end up on YouTube alongside reams of war footage appearing in real time on social media sites. Such clips reveal, among other thing, the presence of American special operators amid forward units, as well as Apache helicopters firing downward – in other words, U.S. forces in combat.

Obama administration officials have struggled to maintain their insistence that U.S. military intervention in Iraq and Syria is limited and putting relatively few Americans in harm’s way. There is nowhere near the 150,000-troop presence at the height of the Iraq War. There are roughly 5,000 U.S. military personnel in Iraq today, but an untold number of other CIA and other U.S. agency operators, specialists, and private military contractors flowing in and out of the region. U.S. military officials in Baghdad on Saturday said that force also includes U.S. artillery units who from afar are striking ISIS positions and providing cover for advancing Iraqi, Kurdish and U.S. forces.

Not on the U.S.-Iraqi battle plan was a massive sulfur leak near the key staging base of Qayyarah West, south of Mosul, causing troops to don gas masks and limit outdoor activity until Pentagon officials could determine if the air was safe. Air samples have been sent to the Defense Threat Reduction Agency, or DTRA, for analysis, said Col. John Dorrian, military spokesman for Combined Joint Task Force-Operation Inherent Resolve, or CJTF-OIR.

“So we’re on the way, I’m encouraged by the progress to day, I’m confident what the result will be,” Carter said. The secretary continues his visit to the region this weekend before heading to Paris and Brussels next week for additional meetings with defense leaders of the ISIS coalition and NATO.