Complicated Shadows: The Life and Music of Elvis Costello by Graeme Thomson (Canongate Books 2004)

Ironically, the two stand-out tracks on the record were the sparsest, the ones that mostly steered clear of sonic gimmicks. 'Pills and Soap' was a stark, stabbing piano track based on Grandmaster Flash's 'The Message', rush-released as a single in May on Elvis's own IMP label and then supposedly deleted - in actual fact, it never was - on the eve of the 1983 general election. Loosely inspired by a film about the abuse of animals which had made Elvis turn vegetarian, it hid a scabarous - if obscure - political viewpoint beneath the surface.

Meanwhile, 'Shipbuilding' stood up against the very best of his recorded output. While always conceding that Robert Wyatt's version was the original, Elvis liked the song so much he wanted it to be heard by the widest number of people possible. To make his version even more distinctive, he visualised a trumpet solo on the track.

Chet Baker wasn't the first choice. Langer recalls that Wynton Marsalis was discussed but wasn't in the country, while a typically undaunted Elvis had Miles Davis as his original first pick, but it so happened that Baker was in London in May playing a residency at The Canteen. His melancholy, melodic trumpet sound and remarkable good looks had made him a 1950's poster boy, but he had since descended into a grim cycle of cocaine and heroin addiction which gripped him until his death in 1988.

By his own admission, Baker had never heard of Elvis Costello, but when Elvis sounded him out at The Canteen, he quickly agreed to play for scale. 'It was a cash deal,' recalled Elvis. 'He just came in; it may well have been the next day.' Elvis offered to double the jazzman's standard union fee, and few could doubt he was worth every penny.

'One of the best things we ever did was 'Shipbuilding',' recalls Bruce Thomas, still moved by the experience many years on. 'That was probably one of the musical high points. Chet Baker, this wizened corpse on death's door, strung out, just played. He followed this bass line and played his solo, so simple, with so much soul in it. It really touched me. It was one of those things that really made me think about how you judge people.'

While Langer concurs that Baker's final contribution as heard on the record was inspirational, he remembers the session being a tough one. 'We recorded the track live, but he kept blowing bum notes when we got to his solo. He was going, "This isn't jazz!" so he couldn't quite get it. That solo is three whole takes - the band as well - edited together, to get it to work. He was pretty spaced out.'