God bless Carol Burnett: She’s never played a Restoration comedy, at least as far as I know, but she has played a haughty dame or three—overplayed them, in fact, to generally hilarious effect, what with the proud face-makings and the pointedly proper seat-takings and the disapproving glares from under the threateningly arched brows.

So there’s not a child of popular culture who won’t immediately recognize Veanne Cox’s lemon-sour Kate Sullen, the pricelessly disenchanted figure at the center of the Shakespeare Theatre Company’s perfectly enchanting production of The Beaux’ Stratagem. She’s the jaded society lady whose grandly severe style La Burnett was sending up in all those deliciously inflated parodies, a gracefully outraged creature serving up disappointed bons mots in a manner so cuttingly elegant you’ll hardly notice the blood. She is, not to put too fine a point on it, intoxicating: I’d carry her off myself if she weren’t so dangerously good with that rapier.

Yes, there are rapiers, and the ladies get a chance to wield ’em, because The Beaux’ Stratagem is that sort of play. There’s also a minister moonlighting as a highway robber, an empty-pocketed aristocrat masquerading as his richer older brother (plus another gent posing as his servant), a drunken sot of a country squire, and a boisterous creature named Lady Bountiful whose amateur medical enthusiasms seem to be taking quite a toll on the trusting local peasants. (She is played, quite naturally, by the invaluable Nancy Robinette, and in the hands of director Michael Kahn, her part in the evening will inevitably involve a battle-ax.)

And then there’s the peerless Mrs. Sullen. Did I say lemon-sour? Rather think of her as a perfect lemon tart: George Farquhar’s sprightly 1707 comedy, in an adaptation begun in the 1930s by Thornton Wilder and completed just recently by Washington-based farceur Ken Ludwig, comes flavored with plenty of zing, but as with any good confection there’s a genuine undertone of sweetness to even things out. That pair of dissolute city rascals scheming to line their pockets with the dowries of the country ladies? They’re good guys at heart, and they fall hard for the ladies’ undeniable charms. The acerbic Mrs. Sullen? A rare flower, trapped in a loveless marriage and just waiting to bloom.

And bloom Cox most emphatically does, in a winningly rangy and wonderfully precise performance as a woman whose heart tells her one thing but whose honor demands another. As Farquhar & Co. engineer the complications that will first tempt her with an unattainable happiness then bring it suddenly within reach, Cox unerringly negotiates the path from a fashionably pinched asperity to a charmingly well-bred glee; the dying fall in her wan “Heigh-ho” at the one extreme is as elegantly funny as the balletic little flourish she adds at the other, when a swain literally sweeps her off her feet.

That swain, in the person of Christopher Innvar’s Jack Archer, is likewise pretty winning; he’s a rogue, sure, but a charming one, all swagger and self-regard, and every bit as ready to bed the innkeeper’s daughter as to marry the quality. (“The man is a walking Babylon,” he says of another character, but the shoe fits.) Kahn has coached the actor through an admirably clear series of complicated impostures, honorable double-crosses, and rousing swordfights in both bedchamber and kitchen. And someone, presumably Ludwig (though it could well be Wilder), has given Archer a couple of direct-address opportunities to engage the audience, of which Innvar takes full and comical advantage.

Julia Coffey’s suitably adorable Dorinda (she’s the heiress whose cash the rascals’ stratagems are aimed at) and Christian Conn’s rakish Tom Aimwell (he’s the one pretending to his older brother’s title and bank account) complete the central foursome; Kahn’s embarrassingly well-appointed cast also features a raft of D.C. favorites, including Floyd King in a flashy little part as a French parson, Colleen Delany as the innkeeper’s comely daughter, Hugh Nees as a slapstick servant, and Rick Foucheux as that double-dealing highwayman and cleric, preaching fire and brimstone on a Sunday while paving his own road to hell all the work-week long.

And then of course there’s Robinette, everyone’s favorite batty lady, nattering on about bone saws and phlebotomies and the various tools and tricks of Lady Bountiful’s trade. (“Remember, ladies, men with fortunes may come and go, but a good head clamp lasts a lifetime.”) Shakespeare Theatre Company design regular Robert Perdziola has outfitted her in an explosive brocaded getup that looks like the love child of an ottoman and a Chinese screen; it’s as dizzying as she is and every bit as much fun. Ditto for James Kronzer’s double-turntable set, a tidy visual analogue for the play’s interlocking puzzle-plots and nicely functional to boot.

The proceedings slow up just a trifle in an extended denouement involving both an informal divorce and several abortive attempts at a hasty wedding, but that’s Restoration comedy for you: The original’s a talky beast, and what’s onstage now has been severely streamlined in the Wilder/Ludwig treatment.

Which, one or two clangorous Ludwig-isms notwithstanding (“I’ve been married 20 years, and at this point a moose with the rickets would look good to me”), turns out to be a pretty solid riot. It’s quick, funny, and still capable of taking a swipe or two at convention; it’s packed with wry observations on the trickiness of human relationships, jabs at the awkward artificialities of class-consciousness, and snarks at the hypocrisies built into the society it portrays. And at its very heart, it’s alive to the very real poignancies and pains lived by women caught in glamorous, empty marriages like that of Mrs. Sullen—which makes it, by my lights, a pretty fine piece of theater.CP