Hearing Leonard Cohen’s music in a movie theater immediately reminds me of Robert Altman’s 1971 film “McCabe and Mrs. Miller.” Eerily appropriate to the film’s western Canadian landscape, the three Cohen songs used – “The Stranger Song,” “Sisters of Mercy,” and “Winter Lady,” all from his 1968 debut – gave Warren Beatty’s shifty frontier pimp a tragic nobility. In Julie Christie’s madam, Mrs. Miller, Mr. Altman found beauty in sleaze, or vice versa; Mr. Cohen has made a career of turning the same trick.

There is nothing so memorable in the new documentary about the Montreal-born songwriter, “Leonard Cohen: I’m Your Man,” but there is plenty to enjoy. Oddly, the hybrid project – part tribute concert, part career retrospective – has its origins in Brooklyn. In 2003, the New York Canadian consulate commissioned the producer Hal Wilner to curate a tribute to Mr. Cohen, to be staged in Prospect Park during its “Celebrate Brooklyn” series.

The show was taken on the road, eventually landing in Sydney, where director Lian Lunson shot it. Ms. Lunson, whose previous credits included a television documentary on Willie Nelson and production on the CD “Songs Inspired by ‘The Passion of the Christ,'” enlisted Mel Gibson (a longtime fan of Mr. Cohen’s, it turns out) as a co-producer and the members of U2 as commentators and sidemen.The result is not much more than the sum of its parts: Interviews with the artist and his acolytes alternate with takes from a night of what amounts to karaoke, though karaoke of a fairly high caliber.

For fans of Mr. Cohen’s songwriting, that is fitting. Mr. Cohen’s reputation has long been dependent on the efforts of other performers. This started with Judy Collins making a folk hit of “Suzanne” in 1967, carried on through Jennifer Warnes’s 1986 “Famous Blue Raincoat” album and into such recent efforts as Rufus Wainwright’s 2004 version of “Hallelujah” (actually a cover, it could be argued, of the late Jeff Buckley’s 1994 cover). Nina Simone, Aaron Neville, the Pixies, R.E.M. – the list goes on.

In 1967, Ms. Collins brought Mr. Cohen to the Newport Folk Festival, which had not seen a talent so poetic since Bob Dylan famously went electric two years before. Already well into his 30s, Mr. Cohen was, in fact, a poet of some reputation in his native country, as well as a writer of fiction, and had spent the previous few years composing the novel “Beautiful Losers” on the tranquil and careless island of Hydra in the Aegean Sea. He descended like Orpheus from these lofty heights to the seedy districts of downtown Manhattan, living at the Chelsea Hotel.

America of the late 1960s turned out to be swarming with hippies. Among them was Janice Joplin, whom Mr. Cohen “ungallantly” disclosed to be the addressee of “Chelsea Hotel No. 2.” This is one of the few episodes the film covers from the period that yielded four albums overflowing with Mr. Cohen’s songs. (His later journey into Buddhism gets twice as much time.) For half a decade, he brewed history and carnality into a headily mystical mix, until 1977’s “Death of a Ladies’ Man,” a collaboration with Phil Spector and his “wall of sound.” With that record, Mr. Cohen acknowledges, he seemed to have grown too decadent, veered too far into the gutter. It turned out to be a punk favorite.

The new documentary might have been subtitled “portrait of the pop star as writer.” There tends to be so little overlap in the fields of literature and popular music that crossover artists are, for good reason, regarded with suspicion. Happy intersections abound – e.g., Lou Reed’s undergraduate apprenticeship to Delmore Schwartz at Syracuse – but most transplants are abortive: Bob Dylan’s “novel” “Tarantula”; poetry by John Lennon, Billy Corgan, and Jewel; Rick Moody in concert. Mr. Cohen is the rare exception – Paul Bowles is another – who fared better on the other side of the divide.

Ms. Lunson lingers over Mr. Cohen’s first attempt at writing, a prayer at his father’s death, and his early literary career. Some of its precious little archival footage shows a young Mr. Cohen rising to the lectern to give a reading.The acolytes bear further witness. Bono testifies to the Cavafian spans of time Mr. Cohen lingers over the composition of lyrics. Nick Cave puts it simply, “He’s a real writer. That’s an advantage.”

Indeed it is. The performers in the Sydney tribute may be a mixed bag, but at least they are restricted to Mr. Cohen’s songbook. Mr. Cave, an obvious Cohen heir with his baritone and his dark posturing, delivers two of the best performances in “Suzanne” and “I’m Your Man.” Mr. Wainwright, his sister Martha in tow, turns in a fine “Chelsea Hotel No. 2,” despite the ironic glimmer in his eye when he hits the line “We are ugly / but we have the music.” Pulp’s Jarvis Cocker ably redeems the title track from “Death of a Ladies’ Man.” The best interpreters of Mr. Cohen’s work, however, have always been women, as Beth Orton (“Sisters of Mercy”) and Linda Thompson (“1,000 Kisses Deep”) prove again.

Lastly, Mr. Cohen himself joins U2 for a somber live-in-the-studio version of “Tower of Song,” after acknowledging he’s open to the idea of touring again. (No surprise, after news that legal battles last year left him broke.) This is a welcome relief after much debating by Bono and the Edge over whether Mr. Cohen is more “spiritual” or “sensual,” “tactile” or “cerebral.” He is the man, after all, who wrote the line “You touched her perfect body with your mind.”