In addition to items from Costello's back catalogue, the album presents songs written for different projects for various kinds of ensembles.[3] The Charles Mingus composition "Hora Decubitus" initially appeared on the album Mingus Mingus Mingus Mingus Mingus. "Upon A Veil of Midnight Blue" would be recorded by the posthumous Charles Mingus Orchestra, initially written for rhythm and blues singer Charles Brown. "Speak Darkly My Angel" was written for Anne Sofie von Otter and the Brodsky Quartet, while "Put Away Forbidden Playthings" was his contribution to a concert commemorating the death of Henry Purcell.[4] A version of "Almost Ideal Eyes" with the Attractions had been an outtake for All This Useless Beauty.
With this album, Costello joined the ranks of songwriters adding lyrics to jazz instrumentals, a practice encompassing classic pop, jazz standards, and vocalese. In addition to the Mingus tune, he drafted words for "Blood Count" by Billy Strayhorn, appearing here as the title song "My Flame Burns Blue."
Ruud Breuls – trumpet solo on "Hora Decubitus," "That's How You Got Killed Before," "Clubland," "Almost Blue," "Almost Ideal Eyes," "Episode of Blonde," "Watching the Detectives"
Bart van Lier – trombone solo on "Hora Decubitus," "That's How You Got Killed Before," "Watching the Detectives"