Where were you the first time you heard “Hallelujah”? Did your parents have a Leonard Cohen record that they spun incessantly? Were you in a dorm room listening to a Jeff Buckley CD? Was it Shrek? It was Shrek, wasn’t it? Wherever you first heard the song, Hallelujah: Leonard Cohen, A Journey, A Song sees you. In an era overstuffed with generic rock biopics and music documentaries, the idea of tracing a song—instead of an artist—is a novel one. There might be no better song for such a treatment than “Hallelujah,” which has lived several lives. It has been embraced by soulful solo artists, singing competition shows, and one ugly green ogre.

Unfortunately, Hallelujah doesn’t commit to its approach. The film wisely opens with a performance of the song in question but then jumps back in time to do a CliffsNotes history of Cohen, covering how he started out as a songwriter, had to be coaxed onstage by his friend Judy Collins, and eventually became an international sensation. Cohen is a compelling figure; there’s a perpetual mystery behind his eyes that draws you in (in essence, he never can be coaxed onstage). But his life, as told here, isn’t particularly compelling. There is a rise and fall. There are drugs, celebrity friends, and a low point when Cohen finds himself middle-aged, single, and broke. And of course, there is a rise again.

If filmmakers Dan Geller and Dayna Goldfine found more drama in his life, the conventional approach might be easier to forgive, but given the film’s title and framing, it feels like a cruel trick. They promise us something new, and give us more of the same. Only in the film’s middle section, when it finally tracks the evolution of the song itself, does Hallelujah live up to its holy promise. We see John Cale of the Velvet Underground pick and choose from among Cohen’s hundreds of verses to create a haunting new “Hallelujah” arranged with just vocals and piano; we hear the story of Buckley, who played his first show at a church and rearranged Cale’s version for the guitar; and, yes, the film acknowledges Shrek, which plays Cale’s version over its timeless montage in which the ogre and donkey aren’t friends anymore.

In this section, the film achieves something like a sense of purpose, but it doesn’t last. A song with just a killer bridge only serves to illuminate the banality of the verses. You might leave Hallelujah thinking that Cohen was a pretty neat guy, but you’ll be dying to know more about Cale, who co-founded one of rock’s most revolutionary groups, and especially Buckley, who released a killer debut album and then tragically drowned while swimming fully clothed in the Mississippi River at 30 years old. You sense in these artists the stuff of great drama, but the film is required by its own structure to gloss over them, and it’s something of a letdown when it returns to Cohen in the final third. 

For Cohen, this might be the natural way of things. He was destined to be a second fiddle, and in the film, he seems oddly at peace with it. It’s fascinating to learn that “Hallelujah” was originally on an album that his U.S. label wouldn’t even release. It only became popular through its reinterpretation. When Alexandra Burke sang it on The X Factor UK in 2008, it sparked yet another resurgence of interest in the song that benefited every artist who ever recorded it. Her version hit No. 1 in the charts, while Buckley’s was at No. 2. Cohen’s peaked at No. 36, confirming that “Hallelujah” is a song meant to be covered rather than sung by its author. If only the film embraced this concept rather than lamenting it.

Hallelujah opens at Landmark’s E Street Cinema and Angelika Film Center Mosaic July 8.