Listed below are the 34 compositions Leo Parker was known to have composed or co-composed. They mainly follow basic forms such as blues and I Got Rhythm changes, and many are riff-based. But their simplicity makes them no less enjoyable. (Click on the recording date to view the session details in the Discography.)
| TITLE | RECORDING DATES |
|---|---|
| Anything Can Happen | August 10, 1953 |
| Blue Leo (co-composed with Ike Quebec) | September 9, 1961 |
| Blue Sails [Parker’s Pal’s] | August 10, 1953 September 9, 1961 |
| Candlelight Serenade | July 4, 1951 |
| Chase ‘n the Lion | March 23, 1948 |
| Cool Leo | November 15, 1952 |
| Dinky | March 23, 1948 |
| Eb Pob [Kilroy’s Bounce, Leo’s Bounce] (co-composed with Fats Navarro) | January 29, 1947 |
| Glad Lad | September 9, 1961 |
| Hornet | July 4, 1951 |
| Ineta [Bootsie] | October 4, 1947 |
| Jam Leo | November 15, 1952 |
| Jumpin’ Leo | October 12, 1961 October 20, 1961 |
| Leapin’ Leo [LG&H] | October 4, 1947 |
| Leo Leaps In | December 28, 1950 |
| Leo’s Bells | March 23, 1948 |
| Leo’s Blues | July 4, 1951 |
| Lion Roars [The Lion’s Roar] | December 19, 1947 September 9, 1961 October 20, 1961 |
| Mad Lad Boogie [Leo’s Boogie] | December 19, 1947 November 15, 1952 |
| Mad Lad Returns | July 20, 1950 October 12, 1961 October 20, 1961 |
| The New Look | March 23, 1948 |
| On the House | March 23, 1948 |
| Reed Rock | July 4, 1951 |
| Rolling with Parker [Rollin’ with Leo] | December 28, 1950 October 12, 1961 October 20, 1961 |
| Señor Leo [Rhumba de Bop] | March 23, 1948 |
| Sweet Talkin’ Leo | March 23, 1948 |
| Swingin’ for Love | March 23, 1948 |
| Talkin’ the Blues | October 20, 1961 |
| TCTB (co-composed with Bill Swindell) | September 9, 1961 |
| Tippin’ Lightly | August 10, 1953 |
| Who’s Mad | July 20, 1950 |
| Wee Dot (unclear if this was composed by J.J. Johnson, or if it was co-composed between Johnson and Parker) | December 19, 1947 |
| Wild Leo | October 4, 1947 |
| Woody [Symphony in Sid] (unclear if this was composed by Illinois Jacquet, or if it was co-composed between Jacquet and Parker) | December 28, 1950 |