David Letterman played Santa Claus -- or, rather, Bob Hope -- on Wednesday by dropping in for a Christmas Eve visit with U.S. troops in Baghdad, reports the Associated Press.

The "Late Show" host joked, of course, as he boosted morale at the military's main combat hospital and greeted soldiers at one of Saddam Hussein's ransacked palaces, which now serves as part of the U.S.-led coalition's headquarters.

Letterman -- accompanied by his comedy sidekick Biff Henderson and his show's lead musician, Paul Schaffer -- arrived at the hospital wearing dark sunglasses, smoking a cigarette, holding a cup of coffee and casually taking a phone call, says the news service.

"He acts like he's been here for years," said 1st Lt. Michael Gerstmyer, 24, from Baltimore, who snapped a picture of the funnyman.

Touring the hospital, Letterman, 56, stopped at the bed of Pfc. Jacob Dominique, 20, of Archbold, Ohio, and was told by a nurse: "We took his appendix."

"I saw it downstairs in the gift shop," was Letterman's snappy reply, which earned him a roomful of laughs.

Typically, he also reeled off a list of the "Top 10 Signs that You've Been in Iraq Too Long."

Among them, said Letterman: "No. 9: You've heard a crazy rumor that Arnold Schwarzenegger is the governor of California."