In a revival of the 2002 musical “A Man of No Importance,” the star of “The Big Bang Theory” achieves something more delicate.You couldn’t have predicted from “Ragtime,” which ran on Broadway for two years in the late 1990s, that its authors would follow up with something as vastly different as “A Man of No Importance.” Yet that’s what Stephen Flaherty and Lynn Ahrens, who wrote the songs, and Terrence McNally, who wrote the book, did in 2002. Their second musical is as quiet, delicate and Irish as its predecessor is loud, meaty and American. Instead of bleating big themes, it ekes feeling from repression in telling the story of a character who does the same.He is Alfie Byrne, a Dublin bus conductor and closeted gay man who in 1964 finds some measure of fulfillment — or at least companionship — among St. Imelda’s Players, the awful amateur theatrical group whose shows he directs in the social hall of his parish church. With Oscar Wilde as his spirit guide, he makes his small-scale art into a life that’s more beautiful than the one the real world gave him.Likewise the lovely revival that opened on Sunday at Classic Stage Company, starring Jim Parsons and directed by John Doyle. Trimmer than the very fine original production at Lincoln Center Theater, and staged on a minimal set (also by Doyle) consisting of a few chairs, mirrors and statuary Marys, it’s a good fit for material that was always modest. Twenty years on, it’s also a good fit for a moment in which closet stories are beginning to lose their currency.In that sense it’s an advantage that Parsons, at 49, is younger by nearly a decade than both Roger Rees, who played Alfie in 2002, and Albert Finney, who originated the role in the 1994 film on which the musical is based. With his confident voice, unlined face and television polish, he never seems hopeless or, viewed from our time, too old for a new start. And after 12 seasons of “The Big Bang Theory,” he knows not only what marks to hit but exactly how to hit them.A.J. Shively, left, as Robbie Fay and Parsons as Alfie Byrne in the musical “A Man Of No Importance” at the Classic Stage Company.Sara Krulwich/The New York TimesAs such, Alfie’s problem is not so much “the love that dare not speak its name” as the personality that won’t shut up. He’s a classic, bossy theatrical misfit, accepted (if only he believed it) at least as much for his oddness as despite it. On the bus each day, he reads poetry to delighted riders, and tries to bring culture even to the handsome young driver he calls, after Wilde’s reckless lover, Bosie — as if the name Robbie Fay weren’t sufficient.At home, though, Alfie locks his bedroom door against the curious eyes of his older sister, Lily, who somehow has not guessed his secret. Lily (Mare Winningham) hopes to marry their neighbor, the butcher Carney (Thom Sesma), but will not do so until her brother is settled. So when Alfie takes an interest in Adele Rice, a new passenger on his bus, Lily tries to push them together, not understanding that Alfie’s interest is purely artistic. He wants Adele (Shereen Ahmed) to play the lead in his new St. Imelda’s production, Wilde’s highly inappropriate “Salome,” with its forbidden lust and “immodest dancing.”The film tells this story straightforwardly if ploddingly, as if it were a bus route. We know from the start that Carney, being a butcher and also a ham, will undermine “Salome,” in which he can only play a minor role. And we know that Adele is not the virginal princess Alfie imagines, nor Robbie fated to be the kissable Jokanaan. The musical paradoxically produces a more streamlined and unpredictable experience by giving it a more ornate frame: McNally’s book imagines Alfie’s story as a production put on by his St. Imelda Players.This allows Flaherty and Ahrens to customize song forms to suit each moment and explore genres that fit the milieu — cue the fiddle and uilleann pipes. Though this occasionally produces some stage Irish mush, it also produces some first-rate musical storytelling in numbers like “Books,” in which Lily and Carney sniff at Alfie’s suspicious habits, and “The Streets of Dublin,” in which Robbie (A.J. Shively) drags Alfie out for a high-spirited night on the town.In allowing for shorter scenes and simpler transitions. McNally’s frame is a perfect match for Doyle’s essentialist aesthetic, in which the first question asked seems to be: How little do we need? (Call it his Small Bang Theory.) As in his 2013 “Passion,” he has shrunk the cast by about a quarter (in this case, from 17 to 13) and the running time similarly. As in his Tony-winning revival of “The Color Purple,” he abjures almost all specific signs of setting. And as in so much of what he directs, particularly his cycle of Stephen Sondheim musicals, he has reduced the band by having some actors play instruments; new orchestrations by Bruce Coughlin mean you never feel cheated.Few shows benefit from all these deprivations at once, and “A Man of No Importance” does suffer slightly in its final third as it begins to reveal too much skeleton. Even if you know the story you may wonder which character an actor is now playing, or whether you’re in the church or the pub. You may also feel the lack of choreography, especially with the fine dancer Shively in the cast.But for the most part, this being a show about the possibilities of even the most minimal stage, a minimal stage makes an apt enough setting, and the style enhances more than it squelches. Doyle even manages the equivalent of a hat trick, when an actor plays a tambourine that, in turn, plays a plate.At their best, Doyle’s small triumphs of restraint and husbandry add up to something large. “The Cuddles Mary Gave,” a song whose title seems to promise sickly sweetness, becomes powerfully specific as performed across the grain, without sentimentality, by William Youmans. Nor have I heard a sound so mournful as the one produced in the show’s saddest moment by the accordion: a wheeze of despair.And with actors of such ample imagination — including Winningham, so vinegary as Lily, and Ahmed so exquisitely reticent as Adele — the circumstances informing trenchant performances need not be visible to the audience. They need only be palpable. The rest is up to us.In other words, Doyle won’t hand us emotion dead on a plate, or even on a tambourine. That approach has earned him lots of fans and detractors since his New York breakthrough with “Sweeney Todd” in 2005; they are often the same people. It’s fitting that as he steps down after six years as Classic Stage’s artistic director, he does so with such a rich example of what he brings to the table — or, rather, takes away from it. I hope he keeps doing so. To adapt a great Sondheim lyric: Give us less to see.A Man of No ImportanceThrough Dec. 18 at Classic Stage Company, Manhattan; classicstage.org. Running time: 1 hour 45 minutes. More