Throughout David Letterman's years as a late night talk show host, he's had a great band to entertain the audience with a seemingly endless supply of cover songs. But there's one major band that they have never played: the Eagles. On his show Friday (Sept. 12) night, Letterman found out why that's the case.

As he says in this video above, Letterman had wanted to have the CBS Orchestra play some Eagles songs, but was told by a staff member that it would have cost too much to get the licensing rights. At first he said that he would pay whatever was necessary, but was quickly shot down by his producer, who said, "I don't think they make exceptions. They have a flat 'no' policy for television."

Naturally, this only made Letterman want to hear them even more, and tried to figure out if there was a loophole. Another member of his staff then pointed out that they could legally play less than three bars of an Eagles song. Then came the process of trying to figure out which hit to play with musical director Paul Shaffer. But the difficulty in trying to choose which ubiquitous Eagles song they were least sick of -- from 'Life in the Fast Lane' to 'Hotel California' to 'Take It Easy' -- caused Letterman to say, "You know what? I'm not that interested anymore."