The rocker dedicated "Longest Days" from his 2008 album, "Life, Death, Love And Freedom", to his fellow Indiana native as the host winds down his final month of broadcasts after more than three decades in late night television.

Prior to his performance, Mellencamp joined Letterman to chat, and the two compared notes on their heart attacks as the singer smoked on the show. "I'm only good at about three or four things," said Mellencamp. "Smoking is my strong suit. I figure my body is so polluted now that nothing could live in there. Cancer would go, 'I'm not going in there.' I'm going to keep smoking." Check out video - here.

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