On Monday, the Justice Department finally released the memo that lays out the legal argument for why the president has the power to target a U.S. citizen for death in the war on terror. But that legal rationale likely wouldn’t extend to the dozens of Americans who have joined the terror group now tearing Iraq apart.

In other words, the now-infamous 2010 “drone memo” wouldn’t extend to the Islamic State of Iraq and al-Sham, or ISIS, two prominent national security lawyers say.

The memo specifically dealt with the legal rationale for striking Anwar al-Awlaki, whom the Obama administration said was an operational leader of al Qaeda’s affiliate in Yemen. (He was killed a year later by a U.S. drone strike.) The 2010 memo says the president’s authority to kill al-Awlaki—despite laws prohibiting the U.S. government from murdering one of its citizens—stems from the 2001 Authorization for the Use of Military Force (AUMF), the declaration of war passed by Congress against al Qaeda and its allied forces.

That law would likely apply to Abdullah al-Shami, the alias of a senior al Qaeda operational planner that The New York Times reported in February was also born in the United States. The Times reported that al-Shami was the first U.S. citizen since al-Awlaki the Obama administration had considered killing. Earlier that month, the Associated Press first reported that the Justice Department was preparing a legal case against an American al Qaeda operative who officials said was planning attacks to kill U.S. citizens with improvised explosive devices.

ISIS, however, is a different story. Last year the group officially broke ties with al Qaeda and has launched attacks on al Qaeda’s formal affiliate in Syria. Indeed, the leader of ISIS, Abu Bakr al-Baghdadi, publicly rebuffed the pleas from al Qaeda’s leader, Ayman al-Zawahiri, to stay out of Syria. In other words, the 2001 AUMF doesn’t really apply to this terror group.

That’s why John Yoo—the former Bush administration Justice Department official who approved the first memos to authorize the waterboarding of al Qaeda detainees—doesn’t believe the argument made in the 2010 al-Awlaki memo could be used to hit Americans who have joined ISIS.

“According to this memo, President Obama could not target a member of ISIS unless ISIS is linked to al Qaeda,” he told The Daily Beast. “That would be a question of fact that, according to this memo, would be for the President and his national security advisers to decide.”

As The Daily Beast reported last month, U.S. intelligence and defense officials now estimate that more than 100 U.S. citizens have joined jihadist groups fighting now in Syria and Iraq, including ISIS. Since fall, senior U.S. intelligence officials have warned that these citizens will pose a significant threat to cause more mayhem if and when they return to the United States.

In Middle East it does not matter all that much whether these ISIS fighters are still aligned with al Qaeda. ISIS’s militia has been able to take over Iraq’s second-largest city, Mosul, and it is marching ever closer to Baghdad.

But for lawyers who specialize in national security law this distinction matters a great deal.

Kevin Jon Heller—a law professor at the University of London who, unlike Yoo, has argued against an expansive interpretation of the president’s inherent wartime authorities in the Constitution—also said the 2010 memo would likely not apply to Americans who have joined ISIS. “The statutory issue depends on whether ISIS is covered by the AUMF,” he said. “I don’t think so, and I don’t think most scholars do, right or left.”

Heller said it was possible that legal experts would differ on whether Obama had the inherent authorities to target Americans who have joined ISIS under Article II of the Constitution, which makes the president the commander in chief of the U.S. military and vests in him the powers to prosecute war.

Heller said he takes a narrow view of those powers but said he was hesitant to speculate whether the president could target a U.S. citizen who joined ISIS based on his inherent wartime authorities. He said the legal question rested on whether that citizen posed an imminent threat and not the nature of the group in question.

The president’s own top lawyers said last month that Obama had the authority he would need to authorize military action against any terrorist group he wanted based on the authorities spelled out in Article II of the Constitution, even if the AUMF was repealed.