The Obama administration’s new strategy for combating the Islamic State militant group terrorizing Iraq and Syria should not limit discussion of putting U.S. boots on the ground, and doesn’t go far enough overall, recently retired U.S. Gen. James Mattis told the House Intelligence Committee on Thursday.

“You just don’t take anything off the table up front, which it appears the administration has tried to do,” said Mattis, who served as the top U.S. general overseeing operations in the Middle East before leaving military service last year.

Mattis appeared before the House along with Ryan Crocker, who was previously posted as the top U.S. diplomat in Iraq, Syria and Afghanistan, and Dafna H. Rand, the deputy director of studies for the Center for a New American Security.

Mattis, who served 41 years in the Marine Corps, said the United States does not necessarily need to send ground troops into Iraq or Syria to engage in direct combat with the Islamic State. For all their brutality, “you don’t have to use the best military” against them because “these people aren’t that good,” the general said.

But broadcasting up front an unwillingness to use ground troops in Iraq, despite an expanded mission there, creates problems, both Mattis and Crocker said.

“Specifically, if this threat to our nation is determined to be as significant as I believe it is, we may not wish to reassure our enemies in advance that they will not see American ‘boots on the ground,’ ” Mattis said. “If a brigade of a our paratroopers or a battalion landing team of our Marines would strengthen our allies at a key juncture and create havoc/humiliation for our adversaries, then we should do what is necessary with our forces that exist for that very purpose.”

Crocker added that he thought it would be best to embed U.S. Special Operations troops in Iraqi military units now. That was the same recommendation that Gen. Lloyd Austin, commander of U.S. Central Command, made to Obama before the president announced his new strategy against the Islamic State last week.

The testimony came during a week of heated discussion about the appropriate U.S. role in Iraq and whether “boots on the ground” should be employed. Gen. Martin Dempsey, chairman of the Joint Chiefs of Staff, said Tuesday that he would recommend using U.S. troops in combat situations if the situation warranted it, leading the White House to quickly reinforce its commitment that the United States will not be not engaging in another ground war there.

Mattis said the Thursday that United States has allies in the Middle East who will likely send troops to assist in Iraq if “we put ourselves out there and lead.” He cited Jordan and the United Arab Emirates as examples.