Downtown Church consists almost entirely of religious and gospel songs. However this cover of a Big Mama Thornton R&B track cataloguing the excesses of an unfaithful, hard-drinking man is the one exception. This was the song producer Buddy Miller played through the PA regularly so as to center Griffin's backing group. She explained with a chuckle why she decided to cover this very secular song on an album contained sacred numbers: "The band was so greasy by the end of that week. I wanted to do it, just to have it. I didn't really think we would get it on the record, and Buddy said, 'Oh, I'll figure out a way.' And he did. I think he also had in mind tipping the hat to skepticism. Not a bad thing to include."
Thornton is best known for cutting Lieber & Stoller's "Hound Dog" before Elvis - it seems she liked animal metaphors.
The song was featured in an episode of True Blood called "I Smell A Rat," which aired in 2010.