Jamaica Say You Will is the fifth studio album by Joe Cocker, released in April 1975.

The songs from the album come from the same sessions that produced the highly acclaimed LP I Can Stand A Little Rain (1974).

It includes participation by Randy Newman; rhythm section on most of the songs is played by the Kingpins, formerly known for being saxophonist King Curtis' backing band, including Bernard "Pretty" Purdie on drums.

"Oh Mama" is pure vocal blues, accompanied by a saxophone.

The album winds up acoustically, with a simply arranged, folk-flavoured tune, "Jack-a-Diamonds".