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As the last musical guest during David Letterman’s 33-year run on late-night TV on Tuesday, Bob Dylan did it his way.

Not “Forever Young,” “Blowin’ in the Wind” or one of his classics.

No the Minnesota icon sang a Frank Sinatra song with a fitting theme, “The Night We Called It a Day,” from Dylan’s current album “Shadows in the Night.” (Sinatra recorded it in 1942, Dylan cut it this year and just released a new noirish video clip of the song. You can see at the bottom of this post.)

Letterman introduced Dylan by saying he taught his son the two most important things in life: “Be nice to other people” and “the greatest songwriter in modern times is Bob Dylan.”

Then, in a raspy wisp of a voice, Dylan sang a pre-modern times tune written by someone else. Oh well.

The performance was fairly typical of Dylan in concert, which means that if you haven’t seen him lately you might have found him a little quirky. He stood there, all billowy curls and glaring eyes, singing into one microphone while another adjacent old-school microphone, in a separate stand, was unused.

At one point, when Donnie Herron played a pedal-steel guitar solo, a skittish Dylan stepped out of the picture and then oddly reappeared. For hardcore Dylan fans, it was a bit reminiscent of his first Letterman appearance in 1984 when performing “Jokerman,” he let his band play on a little long while he tried to grab the appropriate harmonica for a solo.

At song’s end on Tuesday, Letterman shook hands with Dylan, who gave him a dead-fish shake. “Beautiful,” the host announced. And then he leaned toward drummer George Receli and commented: “All brushes,” referring to the kind of sticks used.

Tuesday was a rare talk-show appearance by the Rock and Roll Hall of Famer – his first such performance since he was on “The Late Show with David Letterman” in 1993. He also sang on Letterman in 1984 and, on the host’s 10th anniversary special in ’92, offering “Like a Rolling Stone” backed by an all-star band that included Carole King, Chrissie Hynde, Mavis Staples, Rosanne Cash and Emmylou Harris.

Letterman’s other guest on his penultimate show Tuesday was Bill Murray, who had been his first guest when the talk show premiered on CBS in ’82 and again on NBC in ’93. Always known for making wacky entrances for Dave (there was flying in a Peter Pan costume, driving in a Rolls dressed as Liberace, etc.), Murray emerged from a giant cake, embraced the host in a schmear of frosting and then spread some frosting on faces of audience members.

Letterman then did two entire sit-down interviews segments with Murray covered in frosting (but he was frosting-free in a different suit for Dylan).

Regis Philbin, Letterman’s most frequent guest (about 150 appearances), made an unannounced appearance during the monologue, asking: “Where does this leave Regis?” Said Letterman: “I don’t care.”

Murray was much more maudlin about the end of the Letterman era. After the two comics chugged vodka from a bottle (at Murray’s suggestion), the movie star pleaded with the host. “It’s great for you but what about the rest of us? We just want more Dave. We just want more.”

So Murray headed outside the Ed Sullivan Theatre and asked people on the street to join him in a circle, singing to the tune of “Give Peace a Chance, “All we are saying is more Worldwide Pants,” which is the name of Letterman’s production company.

Letterman will host his final show Wednesday night – with no announced guests but plenty of surprises promised. For more on Letterman, read Star Tribune TV critic Neal Justin’s report.