Two landmarks of the golden age of Broadway musicals are currently on stage in the region. One is probably the most perfectly constructed and unerringly tuneful musical comedy ever. The other is a cheeky homage to probably the most beloved, heart-warming (insert your own adjective) musical ever.

I’m not really a fan of the latter, The Sound of Music, but I’m a sucker for Guys and Dolls, which is now playing at Barrington Stage. This “musical fable of Broadway” is peopled with colorful criminals (who speak in Damon Runyon’s whimsical gangsterese), sassy showgirls and dogged do-gooders. The clockwork plot—the Swerling/Burrows book is as witty and tight as Frank Loesser’s score—turns on a pair of bets and takes us from Times Square street corners to a glitzy burlesque house, a Salvation Army mission and a Havana that was still, in the ’50s, the norteamericanos’ playground.

With many classics, especially one like this, which occupies its own unique universe, it’s hard to do a new production that’s not a reproduction, perhaps with some original flourishes. Barrington’s approach is to say, essentially, “So what?”

John Rando’s staging and Joshua Bergasse’s choreography observe all the show’s Technicolor conventions. So does the 27-member cast (that number is perhaps the most adventurous thing about the show in this era of tight budgets). It stars Matthew Risch as darkly handsome gambler Sky Masterson, Michael Thomas Holmes as twitchy crap-game impresario Nathan Detroit, Morgan James as pretty, prim missionary Sarah Brown, and Leslie Kritzer as blonde adenoidal Adelaide. Of that quartet, I most enjoyed the two women, who found unexpected subtleties in their respective roles.

There are, indeed, some original flourishes—a positively acrobatic “Crapshooters’ Dance” is one—but this revival’s unabashed purpose is not to plough new ground. As artistic director Julie Boyd put it in her opening night speech, “Every once in a while you do a show just for fun.” In that ambition it succeeds, in the words of one of the Broadway grifters, “nicely, nicely.”

So does Fraulein Maria, now at Hartford Stage. The Sound of Music is one of those musical icons that, love it or hate it, is now part of our DNA (go ahead, don’t start singing “Do, Re, Mi” in your head, I dare you). Fraulein Maria is surely the most unusual show you or I will see this summer. A self-described “edgy and fun cabaret romp,” it’s a dance concert set to the 1965 Julie Andrews movie soundtrack.

You’d expect either an oh-so-cute pastiche of the Rodgers and Hammerstein classic or an SNL-style send-up, but it’s neither. Barbara Karger and Michael Preston’s staging of Doug Elkins’ eclectic choreography is witty and irreverent, having fun with the material without making fun of it. There are three Marias—one of them a black male—a tall, tuxedoed master of ceremonies who reappears in various guises, including Gretl, the littlest von Trapp, some cleverly executed group numbers that wink at several modern dance styles, and “Climb Every Mountain” performed as a break-dance routine.

It’s weird, audacious, as unashamed of deconstructing a classic as Barrington Stage is of reconstructing one, and just as much fun.

Fraulein Maria: Through June 26, Hartford Stage, 50 Church Street, Hartford. (860) 527-5151, hartfordstage.org.

Guys and Dolls: Through July 16, Barrington Stage Company, 30 Union St., Pittsfield. (413) 236-8888, barringtonstageco.org.