When I think about the film “Some Like It Hot” — the deservedly classic 1959 cross-dressing comedy co-written and directed by Billy Wilder and starring Tony Curtis, Jack Lemmon, and Marilyn Monroe — the ending always springs first to mind. I’m not alone; it’s iconic. Joe E.

Brown — sporting a perpetual mile-long, closed-mouthed grin — plays Osgood Fielding III, a millionaire who has fallen in love with a woman named Daphne who is actually a man named Jerry, Jack Lemmon in drag. In the last moment of the movie, Daphne/Jerry, having failed to convince Osgood of her/his marriage-defying flaws, pulls off his wig for his supposed fiancé. “I’m a man,” he pronounces, with exasperated finality.

And without missing a beat, Brown’s Osgood replies: “Well, nobody’s perfect.” This musical version of “Some Like It Hot” also isn’t perfect, but it’s pretty darn terrific, a snazzily old-fashioned and fun show with cleverly fashioned story updates, particularly to the screwball romance between Daphne and Osgood. Book writers Matthew Lopez and Amber Ruffin infuse the cross-dressing zaniness with a convincing, and even moving, tale of self-discovery and self-acceptance.

Set during Prohibition, the story starts off in Chicago, with all the Jazz Age art deco design you can imagine on Scott Pask’s set, and colorful period costumes that won Gregg Barnes a Tony Award. Jerry (Tavis Kordell) and his lifelong pal Joe (Matt Loehr) are a couple of itinerant musici.