Take Nicholas Payton, George Benson, Ray Brown, Chick Corea and Wayne Shorter, add them to the music of Clifford Brown, Wes Montgomery, Oscar Peterson, Bud Powell and Lester Young respectively, and you have a relationship which is, to say the least, intriguing.

That is the recipe of the new Ultimate Jazz series. It allows musicians whose creative prowess flowered in the 1960s or beyond, each to compile a CD of music by another famous jazz musician whose influence on him was profound. Not only have the compilers all recorded for Verve Records, but the music they select must be culled solely from its catalogue. Despite this, the connection between each compiler and his respective musician is thoughtful and considered.

The encounter between Wayne Shorter and his subject, Lester Young, is fascinating. In 1958, a youthful Shorter was waiting at the bar to buy a drink after witnessing a performance by Young. Someone exclaimed, "You look like you're from New York" and, turning around, he discovered the voice belonged to Young, who urged a bewildered Shorter to escape to the cellar and drink Cognac with him.

Alone with the man who had affected so many bop musicians, Shorter was reticent about his own musical ambitions. In 1960, a year after Young's alcohol-induced death, Shorter recorded his own composition, "Lester Left Town", with Art Blakey and the Jazz Messengers.

Lester Young was an inventive improviser and the lyrical, rhapsodic sound he forged with his tenor saxophone was as idiosyncratic as the way he held his instrument. Influenced by Frankie Trumbauer, Young, in the late 1930s, became Count Basie's most coveted saxophonist. The earliest recording that Shorter selects, "Lester Leaps Again", is from 1944, the year that many jazz critics cite as the beginning of his decline. Most of the recordings on the CD date from the mid-1950s and, despite his increasing dependence on alcohol, they demonstrate that Young was quite capable of matching his former fluency in these years. Ably supported by Nat "King" Cole, Harry "Sweets" Edison, Oscar Peterson and Jo Jones among others, the music chosen by Shorter shows how much Young's later work has been undervalued.

Although Dale Turner, the tragic figure in the film Round Midnight, was modelled on Young, Bud Powell, the bop pianist, is sometimes considered the authentic prototype for the film's character. The pianist Chick Corea, chooses the music for Bud Powell's CD and concentrates on Powell's original compositions which emphasise his vivacious, intense style and, inescapably, Art Tatum's influence. Powell, who performed with Charlie Parker at the age of 22, studied classical music between the ages of six and 13, and this is most obvious in the five songs that Powell performs solo. The total of 16 songs are presented chronologically and date from 1949, two years before his violent mental breakdown, to 1956

Ray Brown, the bass player and former husband of Ella Fitzgerald, performs with Powell on five songs. He is the only compiler who does not play the same instrument as his subject, but his qualifications are ideal for choosing the songs of Oscar Peterson. Ray Brown and Norman Granz, the founder of Verve Records, discovered the young Peterson performing in Montreal in 1949. Overwhelmed by the pianist's virtuosity, Granz was determined to include him in his formidable concerts, called Jazz At The Philharmonic. They continued recording and performing together for 14 years. The earliest song that Ray Brown chooses is "Love You Madly", recorded in 1956, but the bulk of the music he selects was released between 1961 and 1964. Although he omits any songs from Oscar Peterson's most famous album, Night Train, he includes "Reunion Blues" which reflects the healthy musical relationship between Peterson's group and the Modern Jazz Quartet.

The trumpeter Clifford Brown, inspired by both Dizzy Gillespie and Fats Navarro, made a profound impression on successive trumpeters despite his death in a car crash at the age of 25 on 26 June 1956. The trumpeter Nicholas Payton, who has played with Elvin Jones and performed in the film Kansas City, is in his early twenties. At the age of 12, he immersed himself in Brown's music and admits that he agonised over which of his songs to choose because Brown "doesn't sound bad on anything". The selections, which include songs from the album Clifford Brown with Strings and performances with the jazz vocalists Helen Merrill, Dinah Washington and Sarah Vaughan, all reflect his technical consistency and elegant, joyous style.

Although George Benson was not quite Wes Montgomery's protege, he shared the jazz guitarist's commercial leanings and they were friends. The music Montgomery recorded for Verve Records in the mid-1960s angered some jazz critics, but Benson selects the most engaging songs from this period. The compilation includes "Twisted Blues", where Montgomery's melodic performance is supported by Oliver Nelson's orchestra, three blues-based songs from his excellent collaborations with the organist Jimmy Smith, and a version of John Coltrane's "Impressions", which was intended to remind his critics of his musical dexterity.

The aim of the series is not to create a definitive collection, but to compile a valid, yet less obvious, selection of music. That's what gives this series a strength and a twist that many others lack.

The Ultimate Jazz series of five CDs is released on 16 March by Polygram Records.