Costello said in the liner notes this was a "record of some of my favourite songs performed with some of my favourite musicians."but that he didn't want to record songs that were too familiar. Costello had searched independent record shops: Potter's Music in Richmond, Probe in Liverpool, Rock On in Camden Town, and many American thrift stores and pawn shops to discover albums that he previously had only known from singles or compilations. Costello said he made his best discoveries in what he called "the greatest record collecting store in the world", Village Music in Mill Valley, California.

The title Kojak Variety refers to the name of a variety store in Barbados near where the album was recorded; Costello was amused by the seemingly random name of the enterprise, and in a similar spirit, decided to apply the name to his album.

Strange 2:39

Hidden Charms 3:29

Remove This Doubt 3:52

I Threw It All Away 3:23

Leave My Kitten Alone 3:10

Everybody´s Crying Mercy 4:05

I´ve Been Wrong Before 3:01

Bama-Lama Bama-Loo 2:45

Must You Throw Dirt In My Face 3:49

Pouring Water On A Drowning Man 3:39

The Very Thought Of You 3:42

Payday 2:57

Please Stay 4:49

Running Out Of Fools 3:04

Days 4:54