The Origin Jazz Library released the album Henry Thomas Sing the Texas Blues in 1961 or 1962. The album included Thomas's recording "Honey, Won't You Allow Me One More Chance?" and was probably the source of Dylan's version.
Todd Harvey, in his book The Formative Dylan: Transmission & Stylistic Influences, 1961–1963, analyses how Dylan dropped Thomas's verses, and adapted his choruses, utilising Thomas's AAAC rhyming structure and four 4-bar phrases in 2/4 time. Harvey writes: "The text of Thomas's chorus remained constant throughout the song. Dylan wrote, for the most part, new text resulting in a four bar phrase verse with the fourth phrase acting as a refrain. He increased Thomas's tempo and added his own guitar accompaniment, placing harmonica solos between verses."