If the Iraqi city of Ramadi, which is under imminent threat from ISIS, fell into jihadist hands, would it matter?

According to Army General Martin Dempsey, the chairman of the Joint Chiefs of Staff, not really. The bigger threat, he says, is the other city ISIS is moving in on—the oil-rich central city of Baiji.

On Thursday, both cities came under attack. In Baiji, ISIS claimed it had penetrated the oil refinery. And in Ramadi, ISIS and Iraqi forces are engaged in fierce battles for control of the city center and the government buildings that define it. Thousands of citizens have fled the city, and hospitals are reporting full beds as those injured from strikes, gunfire, and explosives file in.

Ramadi “is not symbolic in any way. It’s not been declared, you know, part of the caliphate on one hand or central to the future of Iraq. But we want to get it back,” Dempsey told reporters Thursday at his first briefing with Defense Secretary Ashton Carter. “I would much rather that Ramadi not fall, but it won’t be the end of a campaign should it fall.

Dempsey’s comments appeared to be a concerted effort to play down the stakes in the vulnerable city. But it appeared that Iraqi and U.S. officials were split about what was a bigger threat. During an appearance at the Center for Strategic and International Studies, Iraqi Prime Minister Haider al Abadi, who finished a three-day visit to Washington on Thursday, called Anbar a priority.

The largest city of western Anbar province, Ramadi was one of the deadliest places for American troops during the U.S. invasion in Iraq.

The latest ISIS offensives come just as Iraqi and U.S. officials were celebrating the defeat of ISIS forces in the central Iraqi city of Tikrit, the hometown of former Iraqi dictator Saddam Hussein and an ISIS and Baathist stronghold. Both Iraqis and U.S. military officials hoped to strike ISIS with a final death knell but could not agree where to do so.

Iraqi officials said it would be better to strike in Anbar province and build a great buffer around Baghdad, which borders the province. U.S. officials have said they believe striking the central city of Baiji, the next city north of Tikrit and along the highway to Mosul, Iraq’s second-largest city and ISIS’s biggest stronghold in Iraq.

“Baiji is part of the Iraqi oil infrastructure,” Dempsey said Thursday. “Once the Iraqis have full control of Baiji, they will control all of their oil infrastructure, both north and south, and deny ISIL the ability to generate revenue through oil. So Baiji is a more strategic target. And that’s why the focus right now is in fact on Baiji.”