“A Folk Tale,” which the Royal Danish Ballet performed Tuesday night at the Kennedy Center Opera House, is exactly that: a story of the folk, of ordinary people in extraordinary circumstances. It is a sophisticated, shadowy garden-party ballet, rather like Hans Christian Andersen meets “A Midsummer Night’s Dream” with a little disquieting Ibsen thrown in. Dance-wise, this is not an evening that delivers flashy pyrotechnics. Rather, one of its chief charms is the subtle way that movement and body language are used to distinguish one type of folk from another.

But we’re not talking only about people in this ballet, which springs from the 1854 original by Danish choreographer August Bournonville but was reworked earlier this year by Artistic Director Nikolaj Hubbe and his associate, Sorella Englund. Half the cast members are fantasy creatures; some of the key characters are trolls. One troll, Birthe, thinks she’s human — as a result of a baby mix-up, she’s been raised in a wealthy landowning family, and at first her ungainliness and beastly temper (she likes to whip servants with her riding crop) seem merely the antics of a grown-up spoiled brat. We learn later that her behavior is the key to her true origins.

Then there’s a human, Hilda, who lives among the trolls (she, too, was part of the mistaken baby swap) and is presumed to be part of their world, though she’s gentle and willowy and moves with a kind of floating grace that no underground creature possesses.

The rest of this story of mistaken identities, greed and the power of true love is complicated. But I’d wager you can follow most of it even without the program notes (though I recommend reading them), because the tale is so well told in the body. The characters are put over with vivid conviction by dancers who seem to have absorbed acting ability through every pore. This is the great and lasting achievement of the Danish ballet tradition.

Not every one of these dancers is a beneficiary of the famed Danish schooling in dramatic projection — for instance, Alba Nadal, whose Birthe is imperious with a colorful dose of mania, is from Spain — so credit is also due Hubbe, the former New York City Ballet star, for sharpening the collective talents. As Hilda, Susanne Grinder is as different from the trolls as the sun is from storms. She is not the strongest technician I’ve ever seen and, in fact, was rather wobbly in spots on Tuesday. But her expressive powers are a delight, and she never forgets who she is onstage. You see this in how elegantly she carries herself, the expansive sweep of her arms, even in how she inclines her neck a little to show a shade of hopelessness in Act 2, after she learns she must marry one of the hairy little trolls.

Grace, such as Grinder demonstrates, is the defining mark of humanity here. Hubbe has secularized the ballet — Bournonville’s original contained Christian references, entwining religious grace with physical grace. But the spiritual message is largely the same. Love, kindness, consideration for others — these traits set the virtuous apart, and so it is that Hilda eventually marries her true intended, Junker Ove, danced as a sensitive, quiet lad by Marcin Kupinski. The nicest guy finishes first here.

That is, unless he’s a troll. Sweet little Viderik, performed Tuesday by the compelling character dancer Lis Jeppesen, is in love with Hilda, but there is no place for him in her happily-ever-after. The look on his rubbery face — and especially the stoop to his furry, misshapen body — is utterly wrenching as he watches the happy nuptials at the end. Prepare yourself.

Poignant as it is, this is not a ballet of high physical drive. The Bournonville style is understated, though the flashes of quicksilver footwork and light, airy jumps in “A Folk Tale” are splendid. Hubbe, who took over in 2008, has said refining the company’s technique is a priority. This production shows us that ballet is a theatrical art, not just an athletic one.

In this unhurried work of subtlety, Mia Stensgaard’s sets and costumes are the most emphatic element and wonderfully so. Her lacy laser-cut designs create intriguing patterns of shadows and light and take us into a world of Victorian pop-up cards with a 21st-century edge. Here, the human realm is not so different from the hidden fairy burrows; one unfolds to reveal the other, challenging our perceptions of both and plunging us into the unsettling origins of folk tales as a way to explain the unexplainable.

And speaking of grace: Denmark’s Queen Margrethe II and Prince Consort Henrik attended the ballet Tuesday night in the president’s box. An accomplished artist, the queen had created the sets and costumes for the more storybook-looking 1991 version of “A Folk Tale” (which the company performed here the following year). It was that production that Hubbe’s replaces. The queen had the magnanimity, I am told by a company representative, to send Hubbe a note complimenting the new designs.

A Folk Tale

will be performed at the Kennedy Center Opera House by the Royal Danish Ballet on Thursday. It will perform “Napoli,” also by August Bournonville, from Friday to Sunday.