"I had really specific ideas for the rhythm parts for this song," Brad Wood, the album's producer, explained to Song Exploder, "and a lot of that comes from Liz's guitar style. She does a lot of accents off the beat, doesn't play on the downbeat. The really obvious thing to do would be to play a drum pattern that hits those accents but I had been taught never overplay."
Wood also explained the Stones' influence on the arrangement: "One of the things that Rolling Stones are so good at is Charlie Watts' drumming. With 'Divorce Song,' I wanted to have an element that complemented and pushed further the accented strumming that Liz does on that song, and that's where the percussion comes in. What makes 'Divorce Song' sound like a Stones song in my mind is that it's got shakers and cabasa playing this odd accent. And every time I hear that start, it sounds like Jimmy Miller, the producer of the Stones, playing the cowbell on 'Honky Tonk Women
.' The whole song starts out with the cowbell and then Charlie comes in with the beat. That's what makes a Stones song for so many people. It's the thing that you would hear first, and we don't have to have a bunch of big rock guitars and bluesy chords - it just needs some of these very essential, it's like the whiff of, like a vapor, of the Rolling Stones' essence."