The Amazing Rhythm Aces' Their Very Best does a better than average job of presenting the group's biggest hits, selected tracks from five albums, and two solo cuts by bandmember Russell Smith. Alongside the hits "Third Rate Romance," "Amazing Grace (Used to Be Her Favorite Song)," and "The End Is Not in Sight (The Cowboy Tune)" are cover versions of "Mystery Train," "Love and Happiness," and "Lipstick Traces." As this compilation contains the Amazing Rhythm Aces's best-known material, it functions as a definitive collection for casual fans.