The members of the National are gracefully-aging Midwestern-transplanted New Yorkers who wear suits a lot, and the same is also true of David Letterman. They’re a natural fit for one another. Today, the National release their grand and confident new album Trouble Will Find Me. And last night, they came through Letterman’s show, playing a dense and inward version of “Don’t Swallow The Cap” with a full complement of string and horn players, as well as Doveman’s Thomas Bartlett on keyboard. (Dave: “A lot going on there.”) Watch it below.

Trouble Will Find Me is out today on 4AD.