The story of how one song got written does not seem like it would make much of a movie — so “I Can Only Imagine” didn’t interest me at all.

Not, that is, until everyone started raving about it. When Rotten Tomatoes, IMDB, Focus on the Family, CinemaScore and lots of trusted friends all recommend a movie, you can be pretty sure the film is doing something right.

In this case, that would include quite a number of things:

While it purports to address the composing of the hit song by MercyMe — which, according to the movie’s credits, is now the best-selling Christian tune of all time — “I Can Only Imagine” does not trot out that hit till its final half-hour, during which we get one and only one blazing rendition; and even that is considerably different than the radio version. So there’s no overkill with a song you’ve already heard a thousand times, and which wasn’t all that lyrically profound to begin with.

Actor J. Michael Finley — recruited after producers saw him playing Jean Valjean onstage in “Les Mis” — does his own singing, and he’s at least as soulful as the original crooner. On top of that, Finley can really act, bringing a grounded humanity to Bart Millard, who struggled with self-doubt, rejection and an abusive home-life before emerging into pop-music superstardom.

Dennis Quaid is sensational, doing some of his best work ever as Millard’s angry, alcoholic father. During the late breakfast scene after Bart returns home one night, Quaid puts on a master-class in acting, taking us through a huge range of emotions, sometimes several in the same moment.

Madeline Carroll helps keep us engaged with her sympathetic portrayal of Millard’s girlfriend, Shannon, while Taegen Burns lights up the screen as young Shannon; and there’s similarly strong work from Brody Rose as young Bart and country star Trace Adkins as MercyMe’s long-suffering manager, Scott Brickell.

Adkins gets the film’s key reflection on creativity, telling Millard that while he has the technical goods, there’s something artificial in his delivery, and he won’t really connect with audiences unless he takes down that barrier and opens up his real, authentic self.

Yet again, this insight is terse and pithy, effective because it isn’t overdone; and I suspect that’s the key to this film’s success: Moving briefly through a wide array of relatable issues — young love, ambition, childhood trauma, forgiveness, artistic integrity, religious conversion — it doesn’t press any of its buttons too long or hard; and in this way, it avoids feeling preachy, mawkish or manipulative.

Having already raked in more than five times its modest $7 million budget, “I Can Only Imagine” proves there’s a solid market for faith-based films made with skill, integrity and respect for their subject.

Especially if that subject is a triple-platinum pop song.

Three stars out of four.