The creative minds behind “Floyd and Clea Under the Western Sky” know that its songs — country-and-western, with a fresh, unfancy twist — are its glory. As sung by the two leads, David Cale (who co-wrote the songs with Jonathan Kreisberg) and the spitfire Mary Faber, the songs are almost good enough to make you forget the whisper-thin story (also by Mr. Cale).

More than anything, director Joe Calarco’s production of “Floyd and Clea” is a testament to the powers of old-fashioned stage presence. It’s hard to think of two more likable performers than Mr. Cale, who gives the washed-up Floyd a gentle, lonesome charm, and Ms. Faber, who invests Clea with her own irresistible sweetness. Their characters may be flimsy on the page, but these singer-actors give them full-bodied onstage personas.

Floyd, a middle-aged burnout with a hip flask, has Woody Allen eyeglasses and a nervous energy that gives him a rabbit-like quiver. His awkwardness is endemic: His big ears poke out from under his cowboy hat, and when he speaks, his drawling voice is full of cracks and froggy notes. Ever the loner, Floyd is living in his car surrounded by snowdrifts (the clever set is by David Korins) when Clea discovers him.

The teenage daughter of a social worker, Clea (who looks like a young Sissy Spacek) has been around addicts plenty of times, so she’s not afraid to approach the homeless guy. Besides, she’s a budding songwriter who performs at the high school gym, and she wants to play his guitar. (She’s only got two chords, but she’s got a voice.)

Clea befriends Floyd, and he in turn teaches her about songwriting. Through Clea, Floyd feels the pull toward life again; she gets him off the drink and back onto the stage — albeit at the high school gym.

Clea is less than half Floyd’s age, so their growing attraction is a complicated one. In the play’s one fine dramatic scene, Clea arranges a hotel room for Floyd on a subzero night. The night feels long, and poignant; soon, Clea will be leaving for Los Angeles to try to become a big star. Lying in Floyd’s bed in a tank top and jeans, smoking a cigarette, Clea tries on her grown-up voice and asks whether Floyd thinks motel rooms are sexy. But they part as friends, with Floyd promising not to drink, and Clea promising to call him on the cell phone she’s left behind.

Sadly, the scene’s subtlety is soon supplanted by the second act’s abrupt, mechanical developments. In L.A., Clea’s success is instantaneous and her descent into Olsen-twin Hollywood hell almost as rapid. A nervous breakdown onstage furnishes the occasion for the only real clunker in the show — the hard-edged, growling “Would You Give a Damn?” Ms. Faber goes for it, belting out the bad-girl ballad, but it still feels like a song on steroids.

I don’t suppose Mr. Cale really expects us to believe that Clea, who left Montana just two songs ago, has become a junkie overnight; the skimpy second act is obviously unfinished. Unfortunately, the play never really earns the poignant scene in which the now-sober Floyd yanks Clea off the highway to hell.

And where does he set her down? In a country-and-western bar, where they go right into a toe-tapping Carter-and-Cash number, and all’s right with the world. The truth is, the songs are awfully good. There’s a story-song for Floyd called “Simple Life” that makes you feel almost as good as if you’d kicked the addiction yourself. There’s a ballad, “White Cowboy Hat,” that’s as nostalgic as rain on a windowpane.

But right now “Floyd and Clea” plays like a handful of singles that could have been a great album. There may be nothing remarkable in that old musical-theater idea of two singers who come alive only onstage, but it still works awfully well, and Mr. Cale should go back and fill in the gaps.

Until December 17 (416 W. 42nd St., between Ninth and Tenth avenues, 212-279-4200).