Quentin Tarantino scored the opening moments of 2003’s Kill Bill: Volume 1 to Nancy Sinatra’s forlorn performance of “Bang Bang (My Baby Shot Me Down)”. It’s a canny pick, even if the title of the Sonny Bono-penned number made it an obvious choice for Hollywood’s pre-eminent record-nerd auteur, who’d just given his viewers their first glimpse of Uma Thurman’s character as she’s shot in the head by her unseen lover. While Sinatra’s voice possesses a delicacy that starkly contrasts with the bloodshed to come, the lyrics hint at darker things, as do the feelings of love, hurt and resignation she conveys so chillingly alongside the trembling tremolo of Billy Strange’s guitar.

As the first of the 23 songs on Start Walkin’: 1965-1976, “Bang Bang” is again being used to begin a story about a woman who should not be underestimated. The compilation inaugurates a reissue campaign by Light In The Attic that continues later this year with newly remastered editions of Sinatra’s 1966 debut long-player Boots, 1968’s majestic Nancy & Lee and 1972’s more autumnal Nancy & Lee Again.

Covering Sinatra’s most productive years with her primary collaborator Lee Hazlewood (already the subject of his own lavish Light In The Attic campaign), Start Walkin’ relates a narrative arc that may be familiar to those who’ve long considered the Chairman of the Board’s eldest daughter to be one of the coolest women to walk the Earth. But the choice of opening note here is as significant for the compilation’s purposes as it was for Tarantino’s. Like the tale of Thurman’s assassin, this one is about earning some payback. This time it’s for a performer whose versatility and artistry have long been overshadowed by the contributions of her illustrious collaborators and by Sinatra’s own celebrity. Indeed, by leading with “Bang Bang” and closing with little-heard marvels made after the hits ran out, Start Walkin’ presents a wider, richer view of a singer who may finally be regarded as more than Hazlewood’s modeling clay or, worse yet, a well-born starlet remembered for those thigh-high go-go boots.

At the very least, the new collection trumps the umpteen greatest-hits albums that preceded it. If Start Walkin’ were more like those sets, it would’ve opened with the song that made Sinatra a star. Initially released at the tail end of 1965 and a chart-topper in the US and UK soon afterward, “These Boots Are Made For Walking” followed Sinatra’s run of singles for her father’s label Reprise that had some chart success in Europe and Japan but made little impact at home. It was Sinatra Sr who connected the singer with Hazlewood, then best known for his work with Duane Eddy. Though the rangy Oklahoman had no lack of opinions, the “skinny Italian girl” – as Hazlewood initially called her to Strange, cheekily avoiding the surname – had a will of her own. It was she who convinced Hazlewood that the lyrics to “Boots” were brutal when he sang them but empowering if she did instead (she also had to lobby to make it an A-side.) The result was a natural-born No 1, its swagger fuelled in equal part by Sinatra’s fierce yet playful delivery and the indelible double-bass hook by Chuck Berghofer, one of the Wrecking Crew greats indispensable during Sinatra’s imperial phase.

The song remains an irresistible display of pop-feminist bravura. As such, it provided a formula for the many similarly strident numbers that can be found throughout the six Sinatra albums that arrived in quick succession through 1966 and 1967. Yet Start Walkin’ emphasises the team’s many deviations from the mean, demonstrating how inventive and subversive Sinatra’s music could be even before her music with Hazlewood took a more avidly idiosyncratic direction with Nancy & Lee. Just consider the decidedly weird nature of 1966’s “Sugar Town”, a dreamy shuffle that hit the Top 10 in the US and the UK which Sinatra later described as Hazlewood’s own “Lucy In The Sky With Diamonds” due to its coy acid references.

The same year’s “Friday’s Child” captures Sinatra in a more dramatic mode, casting herself as a distraught diva in a smoky cabaret. Her power as a vocalist will surprise anyone who figured her skill set was limited to ethereal softness and Sunset Strip sass. After going the full Shirley Bassey on her 1967 Bond theme “You Only Live Twice” – included here in the punchier version cut with the Wrecking Crew in LA rather than John Barry’s orchestra in London – she trumps even the shrieking strings on “Lightning’s Child”, a 1967 single whose synthesis of Wagnerian grandeur and cowboy-musical panache would be campy if not delivered with such ferocity.

On songs like these, Sinatra is indisputably the star of the show. It’s harder to assert that for some of her most famous pairings with Hazlewood. While she’s an amiable sparring partner on their version of “Jackson”, her partner’s bullfrog voice and drawling delivery gives Sinatra less room to manoeuvre in 1966’s “Summer Wine”, the first of their duets to hit the charts, and “Some Velvet Morning”, the mythopoetic masterstroke that Hazlewood originally wrote for the most Ingmar Bergman-esque sequence in 1967’s Movin’ With Nancy TV special.

That’s why some of their lesser-celebrated duets are the greater standouts on Start Walkin’. Shimmering and cosmic, “Sand” is an astonishing demonstration of the balance they could achieve with two voices that no-one in their right mind would have paired. The selections from 1972’s Nancy & Lee Again are similarly extraordinary as examples of how deeply she immersed herself in the songs’ characters. In the almost unbearably poignant “Arkansas Coal (Suite)”, she deftly shifts between the roles of three women in a family blighted by tragedy. And her breakdown at the end of “Down From Dover” – perhaps the most wrenching of the many heartstring-pullers written by Dolly Parton – could make a stone cry.

Sinatra was herself heartbroken when Hazlewood abruptly departed for Sweden in 1968, reportedly fleeing his problems with the IRS and the prospect of a draft letter for his son. Though Sinatra’s career never really recovered from the end of the team’s original run, Start Walkin’ shows she was hardly down for the count. Produced by Jimmy Bowen for her 1972 album Woman, “Kind Of A Woman” has much of the same magic of yore, and the outtake “Machine Gun Kelly” is even better. Released as a single in 1976, Sinatra and Hazlewood’s gorgeous cover of French singer Joe Dassin’s hit “(L’été Indien) Indian Summer” was one in the series of reunions that continued with their tours in the ’90s and 2004’s Nancy & Lee 3.

Knowing that the music business found her “passé”, Sinatra largely left it behind in the ’70s, devoting her energy to her young family instead. The latter-day contents of Start Walkin’ invites thoughts of the music that might’ve been. Given her affinity for then-emergent country-music talents like Mel Tillis and Mac Davis, it’s certainly easy to imagine Sinatra in rhinestones as a strong yet soft-hearted songstress in the vein of Parton and Loretta Lynn. Any further adventures with Hazlewood through the decade would only have gotten weirder if the hypnagogic haze of “Indian Summer” was a fair indication.

But those stories are only of the speculative variety. More compelling by far is the one that’s told here, in 23 concise chapters that are thrilling, surprising and sometimes sublime. You could call the whole saga ‘Once Upon A Time… In Hollywood’ if Tarantino hadn’t gotten there first.