Much like the 1991 film that inspired it, the new musical Dogfight is a sweet, unassuming and quietly touching tale that has the feel of a tightly constructed short story. While its storyline about a young Marine and the plain young woman he first exploits and then falls for doesn’t particularly benefit from musicalization, book writer Peter Duchan and composers Benj Pasek and Justin Paul have done an admirable job of capturing its appeal. This small-scale musical could well become a staple at regional theaters.

Told mostly as flashback and set on in San Francisco on the eve of the1963 Kennedy assassination—a date that has become dramatic shorthand for lost innocence—it concerns a malicious contest held by a trio of young Marines the night before they are scheduled to be deployed to Vietnam. The goal is to secure a date with the ugliest woman, or dog, they can find, with the soldier procuring the most objectionable one winning the prize.

Corporal Eddie Birdlace (Derek Klena) thinks he’s found his winner, meaning a loser, in Rose (Lindsay Mendez), a sweet but plain woman who works as a waitress in her mother’s modest diner. Wooing her by falsely professing a shared love of folk music, he persuades her to accompany him to a party attended by his fellow conspirators.

When Rose becomes aware of the scam thanks to the loose-lipped female accomplice (Annaleigh Ashford) of one of the Marines who’s stacked the decks, she naturally reacts with deep anger and hurt, even telling Eddie that she hopes he dies overseas. But by then he’s fallen for her, and his attempts to make amends lead to a tentative romance even though his idea of an apology is to tell her, “I don’t care what you look like.”

With its tuneful musical score blending sixties-style pop/rock, tender ballads and more sophisticated, Sondheim-influenced songs, the show feels like a bit of a hodgepodge. Such early exuberant numbers as “Some Kinda Time,” featuring energetic choreography by Christopher Gattelli that recalls his Tony Award-winning work for Newsies, at first give the impression that the show is going to sacrifice subtle emotion for bombast. But under the assured direction of Joe Mantello it soon settles down into a more relaxed groove, with such scenes as the couple’s awkward first date at a swanky restaurant proving thoroughly winning.

Much of the credit goes to the two young leads. While he has the unenviable task of trying of match the soulfulness of the film’s River Phoenix, the strong-voiced Klena makes the role his own, and is completely credible as an unsophisticated young soldier who taps into his innate decency. And Mendez, although hardly as unattractive as her character is supposed to be, conveys awkwardness and insecurity in deeply touching fashion.

They’re well supported by the rest of the ensemble, with particularly strong work by Josh Segarra (Lysistrata Jones) and Nick Blaemire as Eddie’s fellow Marines and Ashford as the contestant who spills the beans. 

Second Stage Theatre, 305 W. 43rd St. 212-246-4422. www.2st.com