According to AMG - All Music Guide, OLD WITCH OLD WITCH is included in Burl Ives' album, "A Twinkle in Your Eye," which is still available as a CD (Sony 63420, 1998).

It is attributed to "MacGimsey." This is apparently Robert MacGimsey (1898-1979) who also wrote "Sweet Little Jesus Boy." Evidently MacGimsey made use of traditional material.