When I heard “Sinatra: The Life” (Alfred A. Knopf, 592 pages, $26.95) was being written, my fondest wish was that Frank Sinatra would at last receive the sort of epic treatment given to his predecessor, Bing Crosby, in “A Pocketful of Dreams” by Gary Giddins, and his successor, Elvis Presley, in the marvelous two-volume biography by Peter Guralnick. No one deserves this more than Sinatra, the greatest of all American popular singers.

This isn’t the book I hoped it would be. It is, in fact, not that much different than a book like Kitty Kelley’s “His Way.” “Sinatra: The Life” makes a gratuitous attempt to be more balanced than “His Way”- that is Nelson Riddle gets a page or so rather than a sentence in the Kelley book – and Anthony Summers and Robbyn Swan are more scrupulous researchers and better writers, footnoting every single fact. Yet, like Ms. Kelley, they distort the facts to suit their ends: To link him, once and for all, to organized crime.

The best line in the whole magilla is a quote from Gene di Novi, which the authors actually gleaned from a book by Gene Lees. Di Novi was a jazz pianist and fellow Italian-American whose relationship with Sinatra was extremely brief, but who came up with a gem of an observation: “Italians tend to break down into two kinds of people – Lucky Luciano or Michaelangelo. Frank is an exception – he’s both.”

This reminded me of how Tony Bennett once compared Sinatra to Benvenuto Cellini – indeed, I only know of Cellini because Mr. Bennett gave me a copy of his autobiography, saying Cellini’s history was so similar to Sinatra’s that the 20th-century singer could practically be a reincarnation of the 16th-century artist. Cellini was one of the major sculptors of his time, beloved by the aristocracy as well as the common folk. Yet he just couldn’t stay out of trouble: He was forever sleeping with the wrong nobleman’s wife, and he had a habit of making deadly enemies and even more dangerous friends.

Unlike Sinatra, however, Cellini wrote his memoirs, and they are generally ranked as one of the great autobiographies in literature. Sinatra has had to rely on biographers, and they have usually not served him well. Most books about him – and there are many – contain pages and pages of lurid details about all of his assignations and unsavory affiliations, and only an occasional reference to his art. Mr. Summers and Ms. Swan want you to think that they are uncovering tons of new research, but most of the book is cobbled together from previous publications – including so much from my own book, “Sinatra! The Song Is You,” that even though they acknowledge the borrowing, I can’t help but feel violated.

If Mr. Summers and Ms. Swan really had spent the last few years searching the archives, they might have come up with something worthwhile: a new Sinatra song nobody knew about; a really outstanding concert that no one has heard; the acetates of one of his lost radio shows. Instead, the best they have to offer is new evidence of his mob associations, and the testimony (not all damning) of one or two girlfriends not interviewed by previous biographers.

The book begins, for instance, with a description of Sinatra’s first recording session, in March 1939. He tagged along with a local saxophonist and bandleader, Frank Mane, who was making some private demo discs, and sang one number (“Our Love”).The authors make it seem like no one has heard the record but them – that Mane “kept it in a drawer for 60 years” and that it currently resides in a “locked safe.”

What they don’t say is that Mane taped it for numerous friends, including Sinatra himself, and even though it has never been legally issued it has been bootlegged and circulated all over the world. Every serious Sinatra fan I have ever met has a copy of “Our Love” on CD or LP.

What new information there is in the book mostly concerns organized crime. There is some hitherto unpublished information about Sinatra’s grandfather, Francesco Sinatra, in Sicily. But the authors are more interested in telling us that the Sinatras lived down the street from future godfather Lucky Luciano – although Luciano was only 3 when they left for the new world. Mr. Summers and Ms. Swan are like overambitious district attorneys, determined to establish and re-establish Sinatra’s links to the mafia. They find mobster skeletons in every closet, even hiding under his bed.

To be sure, Sinatra’s relationship with the mob was not one of his more endearing qualities; as Mr. Summers and Ms. Swan show, he grew up surrounded by it, was brought up to respect it, and never quite seemed to fathom that there were other business models. Yet Mr. Summers and Ms. Swan do not show convincingly that it was anything more than a social relationship and a personal fascination of Sinatra’s.

They do not prove the mafia got Sinatra his first important job, with Harry James. They do not offer hard evidence that the mob got Sinatra out of his contract with Tommy Dorsey. They do provide some fairly convincing hearsay that the mob leaned on Hollywood mogul Harry Cohn to give Sinatra his career-saving role in “From Here to Eternity,” but then admit that director Fred Zinnemann already wanted him for the part.

Sinatra did do business with the mafia. So did every popular singer of the time who worked in nightclubs. In the 1920s, Prohibition permitted the mob to take over the nightclub business all over the country, and it continued to run it until the 1950s, when it consolidated its interests in Las Vegas. If you wanted to work in a nightclub, you had to deal with the mafia on some level – as even singers like Mr. Bennett and Mel Torme, who did not share Sinatra’s fascination with the world of wise guys, have explained.

More bothersome to me, however, is that the authors show a basic lack of understanding of the evolution of American popular music. For instance, they note with some accuracy that Sinatra didn’t start regularly appearing in nightclubs, which were controlled by the Italian and the Jewish mafia, until his nosedive period in the early 1950s. But they offer this as evidence of mob support. That’s far from the whole story.

During the 1940s, Sinatra’s primary venues were movie theaters like the New York Paramount. With the rise of television and the fall of the studio system, these cinemas stopped presenting live shows. The only places Sinatra and many other performers could work were clubs. As it happened, this suited his agenda, since his audience was now more mature, while the main events in theaters like the Brooklyn Paramount were rock ‘n’ roll shows. The authors seem completely unaware of this.

I am sure that I would show a similar misunderstanding if I were to attempt a biography of Richard Nixon or J. Edgar Hoover, two of Mr. Summers’s previous subjects. Then again, I’m not planning to attempt any such thing.

The real question that anyone with conspiracy theories about Sinatra needs to answer for me is this: If Sinatra really was created and owned by the Mafia, why did they make just one? If they could create such a successful star of his magnitude, why wouldn’t they have mass-produced as many as the traffic would allow? The mafia was never known to have any aversion to making money.

The truth is, Sinatra was unique. None of the other Italian-American crooners who have admitted playing footsie with the wise guys – people such as Jimmy Roselli or Al Martino – came anywhere near his celestial orbit. Sinatra’s career owed little to either corporate hype or criminal machinations. He was strictly his own creation.