A waltz called “Last Leaf” — with Mr. Richards joining on vocals — celebrates the image of a lone leaf clinging to a tree: “The autumn took the rest but they won’t take me,” Mr. Waits sings. It’s tempting to hear it as a manifesto of stubborn persistence, but Mr. Waits shrugged that off.
“It was a tree, and there was one leaf left on the tree, and I wondered: ‘Wow, if you can make it through winter, you may be here until next year. Wouldn’t that be great, if you were just the only guy that hung on?’ ” he said. “I guess you could say everything’s a metaphor for everything else, but sometimes it’s just what it is. It’s just what it’s about — about a tree.”