"With Frank, what you had was the truth, coming straight at you, and, if you were lucky, there might be some humour attached, too."

In his Beverly Hills bedroom on the evening of May 14, 1998, under a crucifix draped with rosary beads, Frank Sinatra had a massive heart attack. An ambulance rushed him to the hospital, with the driver running several red lights on the way. Fortunately, traffic was unusually light, because half of America was at home watching the final episode of Seinfeld. They got to the emergency room within 10 minutes, but Sinatra died at 10.50pm, aged 82. His last words were "I'm losing".

Sinatra's funeral took place six days later. There were hundreds of stars in attendance, among them Sophia Loren, Gregory Peck, Jack Nicholson, Bob Dylan and Bruce Springsteen. Less famous fans lined the streets outside, many weeping, some clutching album covers, and a sky-writing plane drew an enormous heart in the sky overhead.

After the service, Sinatra was buried at the Desert Memorial Park in Palm Springs, wearing a blue suit to match his famous eyes. Some had suggested his headstone should read "I Did It My Way", but that would have been too cheesy for The Chairman of the Board. Instead it read "The Best is Yet to Come." As Sinatra himself often said, you better get busy living, because dying's a pain in the arse.

But dead he is, which means he's not around to comment on a major new compilation album, Nothing But the Best, containing remastered versions of the best songs from his Reprise Records era.

In Frank's absence, his daughter Nancy has offered to do the talking instead.

"The key quality my dad had was honesty," she says from her home in Los Angeles. "There's a truthfulness to his delivery, so you can hear the essence of the lyrics and the essence of him, too, as a man and as a singer. There's a new version of `Body and Soul' on this record, for example, that's never been released before. It's just so direct and emotional, it couldn't have been sung by anybody else."

Frank Sinatra married his first wife, Nancy Barbato, in 1939, and Nancy Sinatra was born the following year. A son, Frank Sinatra Jr, was born in 1944, and another daughter, Tina, in 1948. Frank Sinatra was married three more times to Ava Gardner in 1951, to Mia Farrow in 1966, and to Barbara Marx in 1976. Widely disliked by the rest of the family, Marx remained with him until his death.

Along the way, Sinatra had many famous affairs, most notably with actresses Lana Turner, Lauren Bacall, Angie Dickinson and Natalie Wood, but always kept in close contact with his kids, especially Nancy, his eldest.

She is now 67, with a wavering voice and a calm and thoughtful manner. She's disarmingly lovely, even getting my address so she could post a CD of her children's songs to my daughter. She's also unusually forthright, happy to discuss personal topics her publicists have requested she not be asked about.

"Well, I admire honesty. Maybe I get that from my dad. With Frank, what you had was the truth, coming straight at you, and, if you were lucky, there might be some humour attached, too. He could be hilarious, but he was also very direct. He said what he thought."

Yes, he did. And he sometimes used projectiles if he felt words weren't enough. Ol' Blue Eyes could be extremely unpredictable, exploding with rage over the slightest provocation. He famously threw a whole tray of glasses at drummer Buddy Rich because he thought he was playing too loud, and once threw fellow `Rat Pack' star Peter Lawford down some stairs. His biographies are littered with tales in which Frank verbally abused people, smashed things, pulled telephones out of walls, slugged impertinent waiters or reporters.

"Sure, he had a temper," says Nancy Sinatra. "But it was always directed at the right person, at least while I was around. What often set him off was a person not doing a professional job. But in all his 60-plus years as a professional, you could probably count his major blow-ups on maybe seven or eight fingers. Even so, the press milked that stuff for all it was worth. What they failed to notice was his generosity. My dad was always engaging in charitable acts. He made anonymous contributions to people in need all the time, but always insisted that nobody be allowed to tell it was him."

Ah, life's little secrets. In this category one might perhaps also situate Frank Sinatra's "complex" relationship with organised crime. Sinatra always denied his mob involvement, but it's well known that he performed at numerous mafia-run clubs and was a good friend of mobsters Lucky Luciano, Rocco Fischetti and Sam Giancana. At the time of his death, Sinatra's FBI file ran to 2403 pages. In knowing tribute, the character Johnny Fontane in The Godfather movie was based on Sinatra.

But whatever he may have been like as a man, there's no debating Frank Sinatra was one hell of a singer. He had swing, he had style; this hot-head was cucumber-cool. His impeccable phrasing brought even the dodgiest show tunes alive, and his bountiful personal stores of sadness and anger and lust gave heat to every syllable.

As this new compilation shows, Sinatra's best songs had a slippery eroticism few other singers could match. He had stamina, too. After scoring his first number one in 1940, Sinatra rode through numerous changes in popular taste and could still knock out a million-selling record in 1994, a few years before his death.

"What made him so special was that he deeply respected the written word and the written note," says Nancy Sinatra. "He could take an ordinary song and make it something marvellous."

Also marvellous, though far less celebrated, is the music made by Nancy herself. Working with eccentric Oklahoma-born producer Lee Hazlewood, Nancy Sinatra made some of the greatest pop records of the 60s. Many remember her best for 1966 hit "These Boots Are Made For Walking", or for 1967's chart-topping "Somethin' Stupid" duet with her dad, but other career highlights include "Sand", "Summer Wine", "Sugartown" and the extraordinary "Some Velvet Morning". "Well, I'm glad you mention those tunes, because a lot of people forget them. Even now, 40 years later, I'm still treated more like Frank's daughter than as a singer in my own right. People insinuate I'm a one-hit wonder, even though I had 21 chart records. I particularly love "Some Velvet Morning". It's a beautiful song, but also melancholy and dark, because that was Lee. He was funny and clever and talented, but he also had a dark side, which added something special to the songs we did together."

Hazlewood died last August. Not long before his death, he told a British reporter he'd turned Nancy Sinatra into a star by "making her sound like a tough little broad. I got her to sing like a 16-year-old girl who screwed truck drivers." Sinatra finds this hilarious. "He didn't put it to me in quite those terms, but that's true. Before I met Lee, I was singing bubblegum music in a high little teenybopper voice, and he made me sing in a range closer to my speaking voice."

Perhaps the sweetest, and certainly the sneakiest, song in Nancy Sinatra's repertoire is "Sugar Town", a delicious pop confection in which the singer talks of leaving her cares behind and drifting off to "shoo-shoo sugar town". I always suspected it was about taking cocaine. "No. It was actually about LSD. In the 60s, LSD was distributed on sugar cubes, so Lee wrote that song, with such a cunning double entendre that many people never knew what it was about. I was never into drugs myself, though everyone else seemed to be in the 60s. I tried marijuana once, but it made me jump out of my skin. I hated it, so I didn't dare try anything stronger. I'd stick with a beer."

Nancy Sinatra giggles like a schoolgirl when I mention how painfully sexy she was in her 20s. But it's true. A curvy bottle-blonde Italian-American Catholic in knee-high boots and mini-skirts or teensy knitted bikinis, her posters and record covers were the last word in 60s steaminess. "Well, sure, the photos they took of me back then became iconic all over the world. Soldiers took my pin-ups to Vietnam inside their helmets. That sexy image was part of the PR push, and it worked, but that doesn't make those records any less special."

She also made seven movies during the 60s, including early biker flick Wild Angels with Peter Fonda, and Speedway with Elvis Presley. "To be honest, those movies were pretty bad. I watch them now and laugh."

Nancy Sinatra left the entertainment business in 1972 to raise a family with her second husband, dancer Hugh Lambert (she now has two daughters, Amanda, 31, and AJ, 32.) Lambert died of cancer in 1985, and Sinatra decided to get back into making music. It wasn't as easy as she had hoped.

"I just couldn't get noticed, which is why I eventually agreed to do a Playboy photo-shoot in 1995. I was already 55 by that time, so it got me on to some talkshows, but things didn't really take off."

What finally kick-started a late career revival was the endorsement of some younger hipsters. A flurry of live bookings followed the release of Quentin Tarantino's first Kill Bill movie in 2003, which used her spectacular version of "Bang Bang" as the theme tune, and the following year saw the release of a self-titled album in which she sang songs written for her by Morrissey, Jarvis Cocker, Elvis Costello and Bono.

"I was amazed those people knew who I was, let alone loved my music, so that album's very special to me.

"I only wish Dad had still been around to hear it. He was a remarkable man, and my greatest sadness is that I wasn't there when he died. Like everybody else, I was at home watching the last Seinfeld show. Dad only lived five blocks from me, and I was planning to go over there after the show, but meanwhile, they took him to the hospital, and our step-mother Barbara did not call us, which is still cause for great resentment in our family.

"The rage I felt that night is something I will never forget. She had nearly an hour to call us so we could be there too, but she didn't call. My dad said to his road manager `Why aren't my children here?' before he died.

"Now, I know that in order to live a happy life you're supposed to let go of your anger and move on, but I was five minutes down the road watching TV while my dad was dying. That's something I will never forget, let along forgive."

Frank Sinatra's Nothing But the Best is released on Friday. We have 25 copies to give away. Email escape@star-times.co.nz with "Sinatra" in the subject line by Friday, May 9.

The Lowdown: Frank Sinatra

BORN: Frances Albert Sinatra, December 12, 1915, Hoboken, New Jersey.

FAMOUS FOR: A 60-year career as one of show business's most influential and interesting figures.

INFAMOUS FOR: His romantic liaisons and alleged connections to the mafia.

PERSONAL LIFE: He had three children to first wife Nancy and married three more times to Ava Gardner, Mia Farrow and Barbara Marx.