Gregory Wooddell as Jack and Anthony Roach as Algernon in the Shakespeare Theatre Company’s production of The Importance of Being Earnest, directed by Keith Baxter. (Scott Suchman)

The new “The Importance of Being Earnest” by the Shakespeare Theatre Company is impeccably done. And if you don’t buy tickets to this amusingly sunny mounting of Oscar Wilde’s exquisitely percolating comedy, you no doubt will be able to catch the next meticulously rendered version or the one after that or . . .

“Earnest” is one of those perfectly constructed confections that, when packaged in appropriately soigné decor and spoken in suitably plummy tones, can’t go very wrong. (The woeful results of veering from the prescription were apparent in Arena Stage’s calamitously vulgar 2004 production.) So here, at the Lansburgh Theatre, director Keith Baxter sees assiduously to the play’s requirements for style and cheek, with a cast headed by a robust Sian Phillips as Lady Bracknell and a look of obsessively groomed English refinement, delightfully engineered by set designer Simon Higlett, wig designer Paul Huntley and costume designer Robert Perdziola.

Making the wry machinations of Wilde’s winking farce seem like child’s play is actually grown-up’s work, and Baxter — the master of insouciance behind the company’s productions of Richard Brinsley Sheridan’s “The Rivals” (2003), Wilde’s “Lady Windermere’s Fan” (2005) and George Bernard Shaw’s “Mrs. Warren’s Profession” (2010) — is the right adult for the occasion.

Baxter’s “Earnest” is spiffing fun, a demonstration over the span of three acts of why the world’s greatest dinner-party conversation would mandate Wilde being seated to your right (with Shakespeare to your left and Tom Stoppard and Dorothy Parker across the table). The director evinces a pinpoint affinity for Wilde’s vinegary repartee, realized here in exchanges establishing that some of our species’ most devastating tactical weaponry is syntactical.

Carried off with noteworthy acumen is the riposte-rich scene pitting Vanessa Morosco’s Gwendolen against Katie Fabel’s Cecily, as they discover the other is also engaged to a man named Ernest (neither of whom is fully in earnest). Morosco and Fabel prove to be so expert at the piquant verbal jousting they might as well be wearing medieval mail under Perdziola’s elegant Victorian finery.

The Shakespeare Theatre Company presents “The Importance of Being Earnest,” directed by Keith Baxter. Through March 9. (Winyan Soo Hoo/The Washington Post)

Let’s stipulate for the record that “Earnest” is not a daring programming choice, and with a calendar that also includes Stephen Sondheim’s “A Funny Thing Happened on the Way to the Forum” and Noel Coward’s “Private Lives,” the Shakespeare Theatre Company seems to have decided that this season, it will stick to the bunny slope. If this reflects a new marketing reality for a classical company that has shown in the past far more ingenuity and boldness in its offerings — last year, it splendidly paired Shakespeare’s “Coriolanus” and Friedrich Schiller’s rarely produced “Wallenstein” — then what we are witnessing is a company’s backing down. In the migration to more popular fare, I guess the questions become: Does anybody notice? And does anybody care?

Certainly, cares tend to be shown the exit in the presence of a well-handled “Earnest,” a play in which no motive or desire can be deemed too shallow, as long as it is expressed by a member of society with the proper attention to breeding and taste. It’s a play in which as big a kerfuffle might occur over who got the last muffin, as who as a baby got left in a handbag in the cloak room of Victoria Station.

Wilde’s 1895 masterpiece — which owed a debt to comedies-of-manners such as “The Rivals” and, at the same time, paved the way for the works of Coward and other 20th-century dramatic stylists and farceurs — portrays a gallery of characters who seem to create problems for themselves simply so that they can employ wit and guile to solve them. As suavely embodied by Anthony Roach and Gregory Wooddell, Algernon Moncrieff and John Worthing are entitled golden boys, silly men of means who gleefully game the class system in the pursuit of Cecily and Gwendolen — women only too happy to become enveloped in the scheming.

Their elders, such as Patricia Connolly’s delectably dizzy Miss Prism, the tutor to Cecily, are on hand to supply thoroughly useless guidance — and to hide as decorously as possible their own basic instincts. The chastiser-in-chief is Worthing’s Aunt Augusta, a.k.a. Lady Bracknell, one of the driest social commentators in theatrical history, a woman so sensitive to public censure that she advises her niece to hurry with her to catch the next train, because “to miss any more might expose us to comment on the platform.”

Imported from Britain for the occasion, Phillips makes a most enjoyable company debut in the role. Fans of the hugely entertaining 1976 BBC series “I, Claudius,” which chronicled the gory reigns of the Caesars, will recall her terrifying performance as Livia, the ruthless empress-wife of Augustus. Still galvanizing in presence and speech, Phillips nevertheless strums some of the gentler chords in Lady Bracknell’s nature: she’s less the intimidating social enforcer than the single-minded guardian of decorum. It’s a slight but not jarring departure from some other Bracknells you might have seen, and in the context of Baxter’s jolly staging, it’s altogether a success.

If this happens to be your first “Earnest,” you’re off to a good start. Other opportunities for seeing it surely will present themselves. But we can be thankful that in delving into the tried and true, the company has produced something truly good.

The Importance of Being Earnest

by Oscar Wilde. Directed by Keith Baxter. Sets, Simon Higlett; costumes, Robert Perdziola; lighting, Peter West; sound, Jason Tratta; composer/arranger, Kim D. Sherman; wigs, Paul Huntley; voice and text, Gary Logan. With Todd Scofield, John O’Creagh, Lee McKenna. About 2 hours 35 minutes. $18-$106. Through March 9 at Lansburgh Theatre, 450 Seventh St. NW. 202-547-1122.