Why though should those tunes seem to be such improbable platforms for jazz improvisation? From the music's earliest days in New Orleans, jazz musicians always played the popular tunes of the day. Songs we think of as 'jazz standards' by composers such as George Gershwin, Cole Porter and Richard Rogers were thoroughly familiar to audiences before they heard the jazz variations on their themes, and were originally so employed for exactly that reason.

The essence of jazz, from the gloriously lyrical concision of Louis Armstrong's choruses on Stardust to John Coltrane's feverishly inventive half-hour-plus reworkings of My Favourite Things, was the transmutation of a familiar melody, good, bad or indifferent, into improvisational gold.

Since the 1960s however, when many jazz musicians reworked Beatles tunes, the whole symbiotic relationship between jazz and the contemporary popular song has deteriorated.

For a serious jazzman to record a recent pop tune today is a rarity. The only notable exceptions I can think of are Miles Davis - who cut Cyndi Lauper's Time After Time and Michael Jackson's Human Nature for 1984's You're Under Arrest - and Herbie Hancock on The New Standard in 1996.

Their approaches though were markedly different. Miles used broadly similar arrangements to the original recordings, substituting his unmistakable horn for the vocal. These were his equivalents to Bye Bye Blackbird and My Funny Valentine for the 1980s.

Hancock, trying to make the same point as Davis and Garcia that new popular tunes can be brought into the jazz canon alongside evergreens, actually proved the opposite.

Taking songs from a hipper selection of artists - Steely Dan, Peter Gabriel, Babyface, Prince and Nirvana - Hancock, in the company of Michael Brecker, John Scofield, Jack de Johnette, Dave Holland and Don Alias, produced arrangements so far removed from the original tunes that most of them might as well not have been there.

So why has jazz largely ceased to feed on the popular song? One possibility is that good new tunes are rarer than they used to be. Quality of composition in the pop world now rates nowhere near as highly as slick production and marketing.

Another is that since the 1960s jazz and pop performers alike have come under increasing pressure to record original compositions - in some respects to the detriment of both genres. Not every good improviser is a good composer.

The third reason is the conservative side of jazz. The old standards have been with us so long that mastering them has become a rite of passage for each new generation of players. With jazz now more than a century old, the keepers of the flame have to look a long way backwards as well as forwards. Yet there is room for good melodies to cross over from the rock and pop to the jazz repertoire - although I don't think How Deep Is Your Love is among them. Garcia and his sidemen make a strong case for both Leon Russell's Superstar and Stevie Wonder's Cause We've Ended As Lovers, which I imagine they learned from the Jeff Beck version. It's cocktail jazz, but then there's nothing wrong with either jazz or cocktails.