One morning during the presidency of George H.W. Bush, Jonna Mendez, then the CIA’s chief of disguise, entered the White House wearing a mask. She had originally disguised herself as an African-American man but decided that mask wouldn’t work, not least because her voice would give her away. Instead, she borrowed the face of a female colleague. “It was a little nerve-racking,” she recalls. “I hadn’t really worn it anywhere.” She sat outside the Oval Office, chewing her pencil through the mask, until the president was ready for his morning intelligence briefing.

Entering the Oval with Brent Scowcroft, the national security adviser, and Robert Gates, the CIA director, Ms. Mendez delivered the briefing without raising the slightest suspicion. “Then I said, I’m going to show you what we’re doing now, the latest technology. I’m going to take it off.” President Bush, himself a former CIA director, told her not to; he wanted to figure it out himself. Mr. Bush stood up from his desk and circled her but couldn’t spot anything amiss.

“So I just took it off,” laughs Ms. Mendez. “I did the Tom Cruise peel before Tom Cruise did. I think they should call it the Jonna Mendez peel.” Several of the masks she created are now at the International Spy Museum in Washington, D.C.