Whether Orson Welles’s “Mr. Arkadin” is a bad movie with great moments or a good movie with dire failings, it is, like much of Welles’s work, mangled, contentious, and undying. Hailed and mocked in its day, “Mr. Arkadin” – released in at least six versions between 1955 and 1962, none approved by Welles – was largely disregarded by its writer-director, who, having lost control in the editing process, insisted that the experience was too painful to belabor. I don’t blame him for trying to shake it off; “Mr. Arkadin” is a troubling film, and not all the troubles can be laid at the door of an impatient producer. Still, it’s been a favorite of mine for more than four decades.

Criterion now weighs in with “The Complete Mr. Arkadin,” a triple-disc confidential report that doesn’t solve the mystery of what Welles hoped to create, but does – through sheer repetition – make a substantial case for the film as a representative Wellesian achievement. The highlight is a new “Comprehensive Version,” edited by Stefan Drossler and Claude Bertemes, five minutes longer than its predecessors and likely to become the preferred edition. Relying, in part, on Welles’s largely elliptical statements, it collates shots from previous versions, reorders scenes, and uses the best 35-mm stock available.

Of the three versions included in this set – the others are the “Corinth” print, discovered by Peter Bogdanovich in 1960 and believed to be the earliest surviving release, and the 1956 European cut known as “Confidential Report” – the new one is the most fluid, dramatic, and logical. Still, as Mr. Drossler notes, “Eighty to ninety percent of the film is the same in each version.” Criterion also includes the 1956 novel, which expands back stories and fills in plot holes. Welles played a shell game with its authorship, accepting or denying credit at whim.

One of Welles’s primary tactics was the unveiling of a mystery, invariably concerning a fallen titan. Several of his films take the form of confidential reports, most notably “Citizen Kane,” though “The Stranger” and “Touch of Evil” also involve investigations, buried secrets, and spying. In “Macbeth,” the witches know the secret and Macbeth must find it out; in “The Trial,” the state knows the secret, and K must find it out. Welles began “Kane” with the Ivan Ilych death of a protagonist, and “The Third Man” opens with the burial of Harry Lime, who isn’t dead but soon will be. By opening with Othello’s funeral, he flashes back to examine a potent man who, like Lime, is living on borrowed time. He does the same with “Arkadin,” beginning with an empty plane and telling how an all-powerful tycoon fell into the void.

But this time he came up with a plot device of his own, which he thought would achieve popular success: the detective as Judas goat. Welles’s Arkadin, a mysterious potentate of finance, hires a seedy blackmailer to investigate his past, feigning amnesia. Obsessed with the good opinion of his daughter, who has just come of age, he needs to learn who, if anyone, can testify to his early years as a white slaver operating with a Polish gang in 1920s Warsaw. As the de facto detective tracks down each witness, none of whom give a damn about Arkadin, they are killed – until the only witness is the detective himself. The basic story could serve as a good, conventional thriller today.

But Welles always burned his fingers on convention. So he cast a minor stage actor, Robert Arden, as the investigator, Van Stratten – and Mr. Arden delivered a performance so utterly charmless that the audience never identifies with him. What’s more, Welles took pains to establish Van Stratten as a doppelganger for the pure villainy of Arkadin: “Maybe I’ll wind up an Arkadin myself someday,” he crows. Then Welles created a fairy-tale subtext, in which Arkadin and his daughter, Raina (played by Welles’s mistress and future wife, the gorgeous, copiously eyebrowed Paola Mori), occupy an El Greco-meets-Disney castle and the ugly American Van Stratten liberates her from “the ogre” by inadvertently manipulating a parricide. Are we still having fun?

Welles also decided on a double-barrel framework. On the one hand, he followed the usual Raymond Chandler progress of the detective, scurrying from one interview to another, picking up threads of information. This allowed Welles to contrast the boorish Arden with some of the most accomplished scene-stealers alive: Akim Tamiroff, Mischa Auer, Michael Redgrave, Peter van Eyck, Suzanne Flon, and Katina Paxinou. They are all richly entertaining and surprising, as is Patricia Medina, as Van Stratten’s girlfriend, whose comment on Spanish penitents (“They must be awful sorry”) is delivered with comic aplomb.

On the other, Welles chose to contort that straight-ahead narrative into an “intricate” system of flashbacks – which the producer negated in the cutting. On this point, I’m inclined to assume that Welles was a bit disingenuous. Most versions, including the comprehensive one, restore some aspect of the flashback plan, and there is nothing too involuted beyond a flashback within the enveloping flashback.

There are, however, some interesting time tricks, including the very first shot: an unexplained dead body on the beach. The editors have included it because Welles told Mr. Bogdanovich that he planned to start the movie that way; it explains the strange opening narration about an unsolved murder that almost toppled a European government. The shot was almost certainly Welles’s comment on the Montesi scandal of 1953, which was kicked off by a woman’s body found on the beach and implicated members of the Italian government. (Among those dragged into it was Alida Valli, who played Welles’s lover in “The Third Man” and may have perjured herself.) The idea is supposed to be that the woman’s death will shake up Van Stratten and rouse the Italian government to look into Arkadin, but it isn’t worked out.

One gets the feeling that several strands weren’t worked out or, for that matter, filmed. How else to explain the dreadful, recurring shots of a ceiling speaker in the closing scenes? The comprehensive version includes two famous anecdotes told by Arkadin at a masquerade ball – one about a graveyard in which tombstones are marked with the dates of friendships, the other about a scorpion and a frog. Yet it is natural to assume that Welles intended to choose one or the other; as it stands, Arkadin comes off as a stand-up entertaining party guests. The first time I saw “Mr. Arkadin,” I assumed that Welles’s wig and beard, the kind of thing you expect to see in a high school production of “Faust,” were part of Arkadin’s masquerade costume, and was thus stymied by his wearing them throughout. I have made peace with his makeup, however; I find I like the fantastic elements telegraphed by it.

As for the novel, Welles surely had some involvement in writing it, even if the original French publication was assembled by critic and translator Maurice Bessy. (According to Criterion’s notes, Welles wrote a serialization of the film for the London Daily Express; has anyone compared those installments with the novel?) For what little it’s worth: In 1980, Vogue editor Leo Lehrman phoned Welles from his office after I expressed admiration for the novel. He asked Welles if he wrote it. Welles: “Did he like it?” Lehrman: “He likes it very much.” Welles: “Then I wrote it!” – followed by volcanic laughter.

Mr. Giddins’s column appears alternate Tuesdays in The New York Sun.