This four-volume digital-only set collects together a mixture of rare and (from the LP era) well-known tracks by Peggy Lee, that have not been digitally available before. The series, which began to appear last year and is now complete, opens when she signed with Capitol in 1944, after leaving Benny Goodman.

Beginning with the song she and her guitarist husband Dave Barbour wrote, ‘What More Can a Woman Do?’, her star quality is immediately apparent – great aural presence, and a beguiling mix of strength and vulnerability. This underlies several early tracks, notably her third (and least well-known) 1946 version of ‘Don’t Be So Mean To Baby’.

There’s plenty of hard-swinging jazz on Volume 2, with (despite a corny backing vocal) Barbour’s band ably supporting her on ‘Happy Music’, the groovy ‘Rock Me To Sleep’ co-written by Benny Carter, and the light touch of Pete Rugulo’s chart for ‘Save Your Sorrow for Tomorrow’. Album three brings us into the 1960s. A sensitive reading of Jimmy Webb’s ‘Didn’t We’, sits alongside some lovely, previously unheard, alternates of ‘A Taste of Honey’ and ‘I’ll Be Seeing You’, the latter with strings, but with plenty of space for her heartfelt vocal.

The fourth volume underlines that during her final Capitol sessions, Lee was as much a popular entertainer as a jazz singer. A few tracks, including duets with Jim Backus (the voice of the cartoon character Mr Magoo) are very far from jazz. Among those that are, two pieces stand out. The ‘live’ album Beauty and the Beat, with George Shearing’s quintet, was entirely re-recorded in the studio, with dubbed in applause. However, this collection includes ‘Always True to You in My Fashion’ from the actual concert in Miami, including Peggy’s banter with the audience. The second significant track, ‘Ja-da’, by ‘10 Cats and a Mouse’, is a studio session on which Peggy plays drums, and every member of the LA studio band plays a different instrument from usual. Vibes player Red Norvo kicks off with a classy piano solo, Benny Carter (on tenor) swaps eights with Billy May (playing trombone) and Eddie Miller (on alto, instead of his usual tenor) does the same with producer/arranger Dave Cavanaugh playing baritone.

Add to that a couple of beautifully-matched vocal duos with Mel Tormé and a further duet with Dean Martin against a classy big band backing, and there is enough jazz interest here to make this final album well worth exploring too.