It sounds like the idea for a bad movie: Talented musician no one cares about disappears. A small group of overseas fans, knowing nothing of his life, endeavors to find him.

That's the story behind Searching for Sugar Man, a documentary about possibly the best singer-songwriter we've never heard of. None of this quiet drama would hold together if the songs weren't so good and the people so endearing. But it does hold together and, over the course of about 90 minutes, Searching for Sugar Man becomes one of the year's most beguiling movies.

After a brief prologue, the story picks up in Detroit with a broke musician named Sixto Rodriguez performing at a club so thick with smoke, a couple local producers, Dennis Coffey and Mike Theodore (who have impressive resumes themselves), could barely see him on stage. But they were entranced by Rodriguez' music and decided to produce him.

The resulting record, Cold Fact, released in 1970, went nowhere. Neither did a follow-up, Coming From Reality, produced by Steve Rowland and released in 1971. Rodriguez then disappeared.

Cut to South Africa in the middle 1970s, where Rodriguez' music is, to hear the participants tell it, as big as Elvis Presley. As record store owner Stephen "Sugar" Segerman says, when you looked through all your friends' record collections, each contained the Beatles' Abbey Road, Simon & Garfunkel's Bridge Over Troubled Water and Rodriguez' Cold Fact.

Because Rodriguez' fans in South Africa knew nothing about him and had little access to information, the legend grew. He burned himself to death on stage; he shot himself in the head on stage and died; the record came to South Africa because an American tourist brought it over and left it with friends.

The story becomes more intriguing when politics gets involved. South Africa's apartheid government banned Cold Fact. Ilse Assmann, a media manager in Johannesburg, shows spots where copies of Cold Fact were literally scratched by censors.

So, do the filmmakers find Rodriguez? Stop reading if you don't want to know (seriously).

Yes. They do. And he's as fascinating as you'd hope, as is his family—three daughters who are just as surprised by his South African celebrity as he is.

Even after the discovery, Rodriguez himself remains something of a mystery. This is a quiet guy who plays guitar for pleasure and works in demolition ("It keeps the blood circulating," he says) but seems bemused by his status halfway across the world.

For Rodriguez's fans, it's a joy. And it's a joy to watch them delight in his presence at a concert. Searching for Sugar Man seems to earn its sugary feeling because we, quite simply want to like this guy, and we're gratified he's not a jerk.

Of course, we'd never know whether he's a jerk, because this documentary is designed to tell a happy story. There is no mention of Rodriguez' ex-wife (or wives or girlfriends) or whether a lack of sales is the only reason he never made it in the music biz.

The on-screen mystery is good enough, though, and director Malik Bendjelloul effectively structures the movie so that, for quite a while, it appears as if Rodriguez may actually be winked out of existence.

How are the songs? In a word, great. Though the recordings contain unfortunate hallmarks of the times—some tracks are drenched in strings, others have brassy horns for no good reason—they're uniformly excellent. Rodriguez sings with a voice that sounds as if Bread's David Gates smoked a million cigarettes and turned into an early Leonard Cohen/Bob Dylan hybrid overnight.

It helps that Rodriguez' screen presence is so confounding (his daughters call him "Rodriguez" on camera instead of "dad") and that his fans are so ebulliently grateful. And, maybe we should be, too, because his music is powerful and this story's a gem.

Directed by Malik Bendjelloul / CCA Cinematheque / PG-13 / 87 min.