Defense Secretary Chuck Hagel says "there were a lot of red flags" that may have been missed in the background of Aaron Alexis, who killed 12 people Monday at the Washington Navy Yard.

Secretary of Defense Chuck Hagel (Rod Lamkey/Getty Images)

And he says investigators will be looking at why they didn't get picked up in the process of giving Alexis security clearance.

He's ordering two reviews of military security and employee screening programs.

But Gen. Martin Dempsey, chairman of the Joint Chiefs of Staff, says he still believes that those who have served in the military shouldn't be stigmatized by having to answer questions about their mental health status.