Over the past two decades, the Scottish director John Doyle has made a specialty of distilling beloved musicals in often stark but exhilarating productions — from “Oklahoma” to “The Color Purple,” along with several Sondheim classics. In a few cases, including his acclaimed revivals of “Sweeney Todd” and “Company,” this strategy has involved having actors double as musicians. 

For his swan song at off-Broadway’s Classic Stage Company, where he completed the last of six seasons as artistic director earlier this year, Mr. Doyle selected “A Man of No Importance,” a lesser-known gem featuring music by Stephen Flaherty and lyrics by Lynn Ahrens — the duo behind “Ragtime” and “Once On This Island,” among other Broadway fan favorites — and a book by the late Terrence McNally, who was their frequent collaborator.

Based on a 1994 film starring Albert Finney, “Importance” follows one Alfie Byrne, a bus conductor and obsessive Oscar Wilde fan in 1960s Dublin, as he tries to stage Wilde’s “Salome” with a group of amateurs who call themselves the St. Imelda’s Players, after the church adjacent to their rehearsal hall, where they have performed other plays.

Alfie’s facing a couple of challenges, though. For starters, the priest and some parishioners are concerned he may be presenting a “dirty play,” what with Salome gyrating before King Herod and all. The middle-aged Alfie, who lives with his sister, is also harboring a secret: a “love that dare not speak its name,” as he puts it (quoting a poem by Lord Alfred “Bosie” Douglas, Wilde’s  lover), for a younger man.

This account of Alfie’s yearnings and foibles, and those of others in his tight-knit community, is at once breezy and moving — qualities enhanced in no small part by Mr. Flaherty’s sweetly haunting music, perfectly suited to the Celtic flavoring provided both in the original production and here, again, in Bruce Coughlin’s lilting orchestrations.

Mr. Doyle has enlisted some superb actors who play musical instruments for supporting parts, among them Kara Mikula, who fiddles nimbly while pouring comic prowess into her role as an exhausted matron, and Da’Von T. Moody, whose bar patron strums a guitar when not flirting with Alfie. The director, who also serves as scenic designer, has them stroll with other players across an assiduously spare set — dominated by wooden chairs that match the stage — and occasionally wander into the audience.

The principals are just as strong, with one unfortunately conspicuous exception. Jim Parsons, the popular and accomplished stage and screen actor who plays Alfie, is repeatedly upstaged by his co-stars. Part of the problem is physical: Although in his late 40s, Mr. Parsons seems about 15 years younger, and while he delivers the proper earnestness — reverently quoting poetry and speaking of “art” with a piety Alfie’s neighbors reserve for prayer — it can come across more as a boyish quality than the product of years spent hiding from the world. 

And while Mr. Parsons is a competent singer (his role doesn’t require a great one), he is overshadowed by the superior chops and charisma of performers such as A.J. Shively, who sizzles scrappily as the bus driver Alfie fancies, and Shereen Ahmed, who brings a glistening soprano and a gentle but firm intelligence to the young woman cast as Salome — a name the characters pronounce, hilariously, as a cross between “salami” and “baloney.”

To his credit, Mr. Parsons manages an easy, often poignant rapport with these fine players, and with others such as Mare Winningham, droll and touching here as Alfie’s concerned older sister, and Thom Sesma, an expert buffoon as the local butcher who courts her, and considers himself the star of the troupe.   

Mr. Sesma also appears, in flashes, as Alfie’s idol. Decked out in Wilde’s trademark hat and cape, he wields the green carnation that came to symbolize the writer more than a century ago, after he asked an actor to wear the flower on opening night of “Lady Windermere’s Fan.”

“Oscar, you burned so brave and bright/But there’s some of us never can,” Alfie sings at one point. Yet the progress made by this musical’s more subdued hero carries its own radiance, and overall, this intimate, lovely production does it justice.