Nacho Duato and his Spanish troupe Compañía Nacional de Danza are now at the Brooklyn Academy of Music, performing three of Mr. Duato’s pieces — 1996’s “Por Vos Muero,” 2002’s “Castrati,” and 2001’s “White Darkness.” As the choreography flashes through styles (Is someone really krumping during that gavotte?) and the dancers move in ways the brain can scarcely stand to process, whose cumulative invention, dexterity, expressivity, and speed can induce vertigo. This is simultaneous physical and mental virtuosity.

The most thrilling piece comes first. The curtain rises on dancers, dressed in flesh-colored leotards and tights, running in slow motion away from us in silence. As a voice intones Garcilaso de la Vega’s 16th-century poetry in Spanish, the ensemble fractures into couples and short solos, only to disappear silently through the black velvet backdrop. As a series of increasingly charming 15th- and 16th-century pavanes, caprices, and even a requiem play, the company reappears in abbreviated Renaissance-wear to frolic through its own versions of archaic Spanish social dance.

Despite traveling the wide stage at BAM, the dancers seem to be appearing from the dark recesses of a church. Nicolás Fischtel keeps them in a smoky blackness, and sudden images glow like icons glimpsed along a processional. But the mood remains resolutely bright. A dancer strums some air lute at his beloved. A woman poses and then vanishes when a man grabs her, like a kitten, by the neck.

A cousin to Jirí Kylián’s work (Mr. Duato has worked and danced with the Nederlands Dans Theater), the Compañía Nacional style springs naturally from the ballet body. Women are in flat slippers, but even without pointe shoes, certain gestures of their épaulement are undeniably classical. Also as with the NDT, the ballet vocabulary is spliced with countless modernist touches — a shuddering shoulder from breakdance, a pivot right out of Michael Jackson’s playbook. On others it might seem incongruous, but here stiff medieval hands combine easily with the loose Alvin Ailey-style knees. Mr. Duato has 30 ideas to our one; he never leaves us time to process the links. At these speeds, styles simply fuse and melt, and refuse to deconstruct.

The most recent piece on the program, “Castrati,” has the same audience-tickling accessibility as Matthew Bourne’s male swans, which is both a compliment and a complaint. Dressed in low-cut cassocks, a stomping phalanx of black priests menace and coax a young boy meant to go under the knife for the glory of song. Since the men of Compañía Nacional have the same miraculous agility as the women, partnering turns into a soaring, athletic event. Partnering of another sort grounds “White Darkness,” which sets most of the company through wheeling, dispassionate patterns while a single couple makes a centerpiece out of anguish.

Both of these pieces maintain the breathtaking spectacle of the company’s style, while tipping slightly into melodrama. Choosing the same overused Vivaldi piece that accompanies diamond commercials was an unfortunate misstep in “Castrati.”

“White Darkness,” meanwhile, involves some seriously telegraphed pleading, but Jaffar Chalabi’s menacing, breathing fabric backdrop transfixed the audience, and the climactic cascade of white sand at the end of the work elicited an audible gasp.

One tip to the watcher: Avoid reading your program. Mr. Duato’s Achilles’s heel is his occasionally overwrought taste, which doesn’t always keep the strict standards of his movement. “Castrati,” for instance, incorporates an actual castration scene (complete with bloody palm), and “theatrical” choices often wind up as heavy velvet curtains or men in wrist cuffs. But aside from the occasionally eyebrow-raising costume choice, almost everything that winds up onstage works impeccably.

The program, however, in its puppyish way, knocks over the applecart. Translations of the de la Vega poems wipe away their mystery and turn the poems into bathetic pulp (“I’m continuously bathed in tears / always breaking the airs with sighs”), and “White Darkness” loses much of its power once we learn the literal meaning of all that strange white sand. While our imaginations have turned it into salt or stylized water or dust, Mr. Duato tells us he means to represent “a reflection on the world of drugs.” The work as a tribute to a loved one who succumbed to narcotics — but any elegiac power dissipates at the slightly sneezy thought of dancers rolling through piles of cocaine.

Until October 20 (30 Lafayette Ave., between Ashland Place and St. Felix Street, Brooklyn, 718-636-4100).