Thank you, Steve, David and Gordon - much appreciated. To my ears, there is some rhythmic affinity between Tarleton's Jig / Willy / Carol and Miller of the Dee, but it's a common rhythm, and I'd want more overlap melodically to suggest a relationship. Simpson doesn't mention the tune of this ballad under any of its titles. That may be because, as my article states, it survives copied into a manuscript rather than as the original broadside print.