Only the Greatest was Jennings eighth LP for RCA in four years. Contrary to the title, it is not a "best of" package, although it does contain the singer's first pair of Top 5 country hits: "Walk On Out of My Mind," which rose to #5, and "Only Daddy That'll Walk the Line, which just missed the #1 spot. Written by Jimmy Bryant, "Only Daddy That'll Walk the Line" was released in July 1968 as the second single from Only the Greatest.Billboard, in a review of the album, said that it and "Walk On Out of My Mind" were "typical of the robust, compelling vocal style" that Jennings became known for. Nathan Brackett and Christian Hoard, in The New Rolling Stone Album Guide, wrote that Jennings began to "really assert his rough-hewn sensibility" on "Only Daddy That'll Walk the Line." The song spent eighteen weeks on the Hot Country Singles charts, peaking at #2 and holding that peak for five weeks.
In Canada, the song reached Number One on the RPM Country Tracks charts for the week ending September 30, 1968. Jennings would perform the song as part of a medley on The Johnny Cash Show. Although the single was Jennings' biggest success yet, he was chafing under the constrictions imposed by RCA, and remained frustrated that the strapping sound of his live shows with his backing band the Waylors was not coming across on record with the studio musicians that played on his recordings.