In this Aug. 29, 2013 photo provided by CBS, actor...

In this Aug. 29, 2013 photo provided by CBS, actor Bill Murray, left, joins host David Letterman on the set of the "Late Show with David Letterman," in New York, as the show celebrates its 20th Anniversary on Thursday, Aug. 39. Murray was the Late Show's first guest 20 years ago. The show airs Thursday, Aug. 29. (AP Photo/CBS, John Paul Filo) MANDATORY CREDIT; NO SALES; NO ARCHIVE; FOR NORTH AMERICAN USE ONLY Credit: AP Photo John Paul Filo

One more for the road? CBS and David Letterman this afternoon announced a one-year extension that will keep "Late Show with David Letterman" on the air through 2015.

"Les [Moonves] and I had a lengthy discussion, and we both agreed that I needed a little more time to fully run the show into the ground,” said Letterman in a characteristically deadpan statement, while Moonves - CBS president and CEO - added, “There is only one Dave, and we are extremely proud that he continues to call CBS ‘home.'"

Moonves had indicated - strongly - in recent months that a renewal was forthcoming. At the recent press tour in Beverly Hills, he was asked about Letterman's future, and responded: "Other than Johnny Carson, he's probably the best that ever was. We like the stability. We like the relationship we have with Dave. He's our guy and despite what people think, we don't like drama at 11:30."

That was a not so veiled reference to the drama at NBC, which once again presents an opportunity for Letterman - and CBS - much as it did when Jay Leno stepped aside for Conan O'Brien in 2009. Jimmy Fallon will become the "Tonight Show" host in February and - much as they did in 2009 - longtime Jay Leno viewers could sample other shows, which could provide a windfall for "Late Show.".

At 66, Dave is indeed the dean: Twenty years at "Late Show," and thirty-one years since “Late Night with David Letterman” premiered on NBC on Feb. 1, 1982. He has hinted at retirement before - telling Howard Stern, for example, during a 2011 interview, that he might step down in two years (or 2013.) But Letterman clearly continues to relish the job, and his fans continue to relish him: CBS also said his 2013 fall season opening week audience increased 5 percent, to 3.14 million viewers.

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