Thorough, it’s not, but the concert documentary Leonard Cohen: I’m Your Man gathers solid interviews, anecdotes, recitations and tribute performances that present a fairly engaging portrait of the wry, dark Canadian poet who became a distinct voice in pop music.

I’m Your Man is unlikely to appeal much beyond Cohen’s fan base or convert others to the brooding whimsy and dense wordplay of his songs. The movie succeeds in matching his sobering lyricism with kindred spirits who do justice to his tunes during a concert in his honor.

Fellow somber travelers such as Nick Cave, Kate and Anna McGarrigle, Rufus and Martha Wainwright and Beth Orton are among those covering songs that span most of Cohen’s 40-year career.

The reclusive Cohen offers warm and amusing recollections and teams with U2 for a version of Tower of Song as the documentary’s musical finale, although the strangely cloistered, unsatisfying cover winds up anticlimactic after some grand live renditions by other performers.

Music-video maker and former actress Lian Lunson captures the "Came so Far for Beauty" concert at the Sydney (Australia) Opera House in 2005.

Interspersed among the performances are frank, wistful segments with Cohen, who also recites some of his poetry. He discusses his boyhood, his father’s death, the Montreal poetry scene, his spiritual quest with a Zen master and the woman who inspired one of his best-known songs, Suzanne.

Cohen, whose bass vocals often lean more toward talking than singing, also touches on his musical abilities.

"I had the title ‘poet,’ and maybe I was one for a while. Also the title ‘singer’ was kindly accorded me, even though I could barely carry a tune," he recites from one of his poems.

Even so, trained singers have trouble approaching his soulful depth when covering his songs. Music producer Hal Willner assembles musicians who deeply respect Cohen’s songs.

Cave energetically sings I’m Your Man and does a hushed Suzanne. The McGarrigle sisters and Martha Wainwright (daughter of Kate McGarrigle and Loudon Wainwright III) lend beautiful, trilling harmonies to Winter Lady; and Wainwright, brother Rufus and Joan Wasser trade passionate verses on Hallelujah.

Annoyingly, Lunson drops interview segments into the middle of some performances, although she thankfully leaves intact the two standouts: Orton’s achingly gorgeous rendition of Sisters of Mercy and Julie Christensen and Perla Batalla’s duet on Anthem.

Interviews with the musicians are a mixed bag. Rufus Wainwright vividly relates the first time he met Cohen, who was in his underwear, feeding tidbits of sausage to a sickly baby bird. Cave talks with wonder about the transformative day when a friend played him Cohen’s album Songs of Love and Hate.

U2 frontman Bono and guitarist the Edge have some nice insights, yet both go overboard in their fawning praise. Bono redeems himself with this summation of Cohen’s grim yet playful sensibilities:

"A lot of writers have dared to walk up the edge of reason and stared into that great chasm, into the abyss," he says. "Very few people have got there and kind of laughed out loud at what they saw."