The first half of the exhibition “Rococo: The Continuing Curve, 1730–2008,” which just opened at the Cooper-Hewitt, National Design Museum, is absolutely stunning. No matter how austere your aesthetic sensibilities, “Rococo” has enough fine-tuned dreamy opulence and pizzazz to make even the most ascetic among us swoon and grow a little wobbly in the knees.

The show, organized by the Cooper-Hewitt’s Sarah Coffin, Gail Davidson, and Ellen Lupton, and guest curator Penelope Hunter-Stiebel, is brimming with dazzling, mostly 18th-century objects. It includes porcelains, tableware, candelabras, mirrors, snuffboxes, clocks, ironwork, jewelry, furniture, textiles, an altar, a sedan chair, and works on paper. But the best of these objects, though exuberant and extravagant, are well-mannered and restrained. They are aristocratic or court objects; and because of their station, they stop just short of being outlandish. Their wind-whipped, gilt-bronze, and solid silver curlicues, spinning S-curves, and bacchanalian embellishments never quite go over the top; at the very last moment, they appear to relax and to behave themselves, to bow with decorum.

The period of Rococo is a style labeled out of derision at the end of the 18th century by Maurice Quai, a student of the Neoclassicist Jacques-Louis David. The term derives from the French rocaille, meaning rock-and shell-work used for the decoration of grottoes and fountains, as well as from barocco, the Italian word for Baroque, and refers mainly to a whimsical, sometimes frivolous overall decorative scheme favored by Mme. de Pompadour, the mistress of Louis XV (r. 1715–74). The movement, which is said to have begun in France with the work of the great silversmith Juste-Aurèle Meissonnier (his pieces are a highlight of the exhibition), was quite popular, spreading to England, Italy, Germany, Spain, Portugal, the Netherlands, and America. This show’s mission is to trace — with approximately 375 objects — Rococo’s development, its birth and rebirth, throughout the world to the present day.

It may take some time to warm to the flamboyance of many of the works in the show: Why, you might ask, does a commode need to curve into an almost threatening presence; why does a gilt-bronze candelabrum have to spin like a whirling dervish and to be made of trees, balustrades, birds, leaves, vines, and fluttering putti? Usefulness appears to give way to ornament. But it is important to remember that these objects would have been seen originally only in natural light or candlelight, and thus their overactive forms and surfaces would have registered in flashes instead of hitting us full-on.

The best Rococo works in the show have a Mozartian lightness of step under their fanfare. Many of the objects here were used in private apartments, and their color scheme — polished silver and gold, cream, rose pink, and sky blue — as well as their sense of wild nature refined, activates small spaces without overwhelming them. Nothing in Rococo is ever really what it seems: Ballfooted claw feet evoke fur, flames, smoke, and vines; heavy, ornate dressers appear to have alighted like birds. Movement never ceases in these objects, in which every concavity is answered by convexity; in which one full-blown asymmetry is topped by another. But that movement feels rational, playful, even natural.

A carved, gilt wood “Mirror” frame (English, c. 1755), after a design by Thomas Johnson, appears to crawl up the wall. It is a Surreal, foliate lineage of twisting golden seashells, vines, vases, hanging moss, finials, leaves, trees, a portrait bust, and architecture. A hunter, as if he had climbed up the frame’s rocky façade, reclines near the top, holding a dead rabbit, as his dogs bay at him from a lower level.

The back of a German garden “Armchair” (c. 1761–68) is a golden trunk that frames white latticework, through which press forward gilded leaves and vines. A squat, ornate Venetian “Writing Desk” (c. 1760), in gold and turquoise blue, is as heavy as a hippo but, when its doors open, it spreads and lifts like a butterfly. In an 18th-century French daybed, its back and arms wrap around its cushions, closing in on them like a giant shell. And in a Parisian chest of drawers by Jean-Pierre Latz (c. 1745), the full-bellied drawer fronts swell like an ocean surge. The tulipwood marquetry is flying wings, leaves, and flames. The flecked marble top flickers like light on water, and the chest is framed and accented with fiery, gilt-bronze dragon tails, claw feet, and drawer pulls. But its garishness, as in so many objects in this show, is subsumed by its ability to keep your eyes and mind moving and dancing through its beautiful arabesques and across its captivating surfaces.

It is in the second half of this show, when the curators consider Rococo’s “continuing curve,” that problems, or at least distortions and simplifications, arise. Here, the trajectory of an artistic “style,” the Rococo curve, is taken out of context and seen as independent from the very artists who continue to keep the aesthetic forms of that style in motion. The Rococo curve, and every curve hence, pared down through art-historical revisionism, becomes a single long arc that encompasses everything from biomorphic abstraction to 1960s psychedelia.

To suggest, as “Rococo” does, that the S-curve meant the same thing to Fragonard, Watteau, Tiepolo, Meissonnier, Louis Comfort Tiffany, Alvar Aalto, and Charles and Ray Eames; or that it means the same thing in a painting, an altar, an 18th-century window grill, an Art Nouveau lamp, a psychedelic poster, and the whole of Sèvres porcelain — is to do more than put form over function. It is to reduce art and design to its lowest common denominator. When I got to the second floor, where the visitor is greeted by Jeff Koons’s gilded wood “Mirror: Christ and the Lamb” (1988), in which Rococo openness, lightness, and natural movement have slowed to a dead halt and collapsed in on themselves, I felt as if the curators, to bring their thesis up to date, were grasping at contemporary straws.

I will grant that the gilt-bronze “Loïe Fuller Lamp” (c. 1896), one of the hallmarks of French Art Nouveau, looks as if it could have been made a century earlier. But to suggest that Charles and Ray Eames’s 20th-century fiberglass “La Chaise,” which floats like a cloud, or that Alto’s “Savoy Vase,” or that Henry van de Velde’s “Tropon est L’Aliment le Plus Concentré” (1898), possibly the first purely abstract poster, are all direct continuations of the Rococo curve, is to reduce a very complicated series of art movements into one easy arabesque.

A number of the works in the extensive second half of “Rococo” are worthwhile. But to see them all as links in the continuing Rococo chain is to ignore the cross-pollination that happens between art movements and cultures. It is to ignore how artists and designers are inspired, as well as how they think.

“Rococo” gives us no real sense of where the movement comes from. After it gets going, the show nods only in the wall text to the enormous influence of Japanese prints on Art Nouveau. It ignores the impact of the machine aesthetic on art and design, as well as the impact, through the Arts and Crafts Movement, of the interlocking, lacertine imagery of Medieval Hiberno-Saxon manuscripts — especially the manuscripts’ insistence on abstract flatness — on the art of the late 19th century. And it chooses to overlook that Modernism’s aim — though wildly different in different hands — was to move toward purity, not an embellishment, of means. Aalto’s curve, inspired by Arp, was an abstract distillation of the world, not a mere fragment of Rococo elaborations.

“Rococo,” which moves from curve to curve to curve effortlessly through the centuries, progresses smoothly and easily. To do so, however, it ignores the factual bumps in the road.

Until July 6 (2 E. 91st St., between Fifth and Madison avenues, 212-849-8400).