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My Fair Lady does, as it happens, live up to its own moniker: The touring version of Trevor Nunn’s London revival, ensconced for the nonce at the Kennedy Center Opera House, turns out to be pretty fair indeed.

The familiar tale of the brusque patrician diction coach and the grimy cockney girl he coaches into respectability has been handsomely upholstered and briskly updated with all manner of sociologically telling touches—though not, thank God, too aggressively conceptualized, as other revivals in the last few years have been. The principals are basically charming—you’ll forgive Christopher Cazenove’s breath-control issues once Lisa O’Hare’s startlingly Audrey Hepburn–esque glamour captivates you at the embassy ball. And the best thing about this revival is that Nunn seems to have come at an acknowledged classic of the genre as if he were encountering it for the first time, in this century, rather than excavating it from the middle of the last.

It moves with startling quickness—essential, no doubt, for an old-school musical comedy in an era of endemic audience ADD and expensive union-overtime rules. But the updated orchestrations seem decidedly modern too, replacing the original’s swirly, swoony sumptuousness with a decidedly moodier palette of sounds, the better to seduce the disaffected postmodern ear.

And Nunn’s fluid-verging-on-cinematic staging moves much more like, say, Les Misérables than like The Music Man. Speaking of which: Watch the rousing, raunchy “Get Me to the Church” (and its sibling number, “With a Little Bit of Luck”) and you’ll certainly remember who staged the cheerfully filthy-minded “Master of the House” for that French-fried epic: It’s a safe bet Alfred P. Doolittle never thought of celebrating the eve of his wedding with a visit to a whorehouse before Trevor Nunn sent him there.

Besides which, let’s not forget, the show is pretty much the pinnacle of its type: The impossibly well-crafted tunes hang beautifully on that rock-solid book (itself derived, after all, from the sturdy bones of George Bernard Shaw’s play), with snappy dialogue blooming naturally into lyrics that sparkle with wit.

And such songs! “Wouldn’t It Be Loverly?,” “The Rain in Spain,” “On the Street Where You Live,” plus the two above. Come to think of it, the only lady in town with more instantly familiar hits in her pocket is Ella—and she’s drawing on the entire damn American songbook for her set list.