A visitor walks through the Prado Museum's new extensionFor many years, the Prado was almost a secret in plain sight. Years of Spanish isolation, neglect under Franco, then institutional incompetence, compounded the impression of narcolepsy. Melancholy reports of leaks in the ceiling, or yet another director promising change before evaporating, overshadowed the odd loan exhibition. Save for busloads of Japanese tourists, the world simply seemed to pass the Prado by.Truth be told, it was nice. While every other museum concocted Monet blockbusters and fancy new buildings by celebrity architects to name after trustees and satisfy the bean counters who judge success by the number of visitors through the turnstiles rather than by the quality and care of the collection, the Prado stuck with Velázquez and Goya and Titian and Tintoretto in rooms of increasingly shabby grandeur. Before such pictures, nothing else really mattered. That was then. The Prado has in the last several years hired a crew of gifted young curators under an ambitious young director with Byronic good looks named Miguel Zugaza. Now there’s a serious and world-class exhibition program, more than two million visitors annually (this year a record number is expected) — and, just opening, a 237,000-square-foot extension. It’s said to have cost several times more than was budgeted; but then, so did your kitchen. The final price tag was $219 million. Devised by the 70-year-old Spanish architect Rafael Moneo, it moves the museum, stuck so long in the 19th century, into the 21st by modernizing and rationalizing what had become, willy-nilly, a haphazard and disorganized physical plant.Before, whenever an exhibition went up, some of the permanent collection had to come down. Galleries became storage rooms for lack of better places to put the art. Visitors came through side doors not designed to handle mobs, because there was no functional main entrance.A view of the new building at the Prado MuseumThe extension, by freeing up space in the original building (half again as many paintings will have room to go on view), deals with such unglamorous necessities as a new, centralized point of entry, rooms for temporary shows (totaling 15,000 square feet, no minor addition), a lecture hall and — replacing a gulag-style basement cafeteria — a new cafe, all black marble and wood. The cafe is comically small, which actually speaks well of the museum’s priorities. The whole enterprise has the remarkable (for these days) goal of letting the museum do what a museum is supposed to: show its collection better. The plan is so conservative that it’s radical. The old Prado, a stolid neo-Classical behemoth with various expansions added to it since the early 19th century, naturally became an object of Spanish veneration over the years. Frankly, it’s not a particularly graceful work of architecture, but love is blind. The museum’s new, centralized entrance smartly revives Juan de Villanueva’s original 1785 plan, connecting what’s called the Velázquez door, facing one of Madrid’s great boulevards, to a new vestibule. The vestibule is shaped like an apse, in stone and bronze, with walls colored what Mr. Moneo calls Pompeiian red, although you might find yourself thinking of a watermelon. From the vestibule, Mr. Moneo leads visitors toward a second, huge wedge-shape lobby, cut into the slope behind the old museum, with a bronze ceiling and floor-to-ceiling windows. From here you reach the new galleries for temporary shows.The structure’s best feature is a rooftop garden, fitted seamlessly into the streetscape and planted with handsome box hedges. The plan otherwise plainly solves a thorny architectural problem: how to shoehorn various basic services underground and behind the old building, then connect the old museum to a 17th-century cloister a block away. The cloister of the Jerónimos, as it’s called, long a local wreck, became cannon fodder for the French 200 years ago and was left to crumble under Franco. Nobody paid much heed before the museum announced in the 1990s that it would take over the site, after which neighbors, foreseeing years of noisy construction, declared the expansion plan a sacrilege. Endless haggling and a slew of editorial jeremiads unfolded over the better part of a decade. Mr. Moneo finessed the preservation issue by burrowing below ground for the temporary exhibition galleries so that the cloister, now restored, sits on top, exactly where it always was. It’s enclosed, below a skylight, and incorporated as a kind of giant ready-made sculpture into the museum, which silences critics who argue that the cloister needed saving, even if the solution somewhat sterilizes the site. Meanwhile, the glass-and-steel light well that Mr. Moneo cut through the cloister’s floor provides windows for the galleries, relieving them of some of the claustrophobia always felt in underground spaces. From the street, all you see is an exterior of brick, glass and stone, austere and anonymous architecture, discreet but rich, blending quietly into the neighborhood. The one theatrical flourish: a luxuriant pair of massive bronze doors, molded as thickets of vines, by the artist Cristina Iglesias.I suspect there will soon be talk about further extensions, as there always is after a museum expands. Spaniards might want to think twice now. It’s worth recalling that the Prado was never meant to be encyclopedic like the Metropolitan or the Louvre. It began as a royal collection, overseen not by art historians but by court painters like Velázquez and Goya, the best possible curators, and this legacy of private taste, combined with long isolation, assured singularity. You just can’t know great painting unless you’ve been here. That’s the biggest compliment any art museum could be paid. It would be a pity if the Prado, flush with ambition and the prospect of yet another million tourists, diluted its focus.For the moment there’s plenty fresh to see. Hellenistic statues from Tivoli greet visitors in the watermelon vestibule, reminding everybody that the museum has always had great sculpture, not just paintings. Contemporary artists aside from Ms. Iglesias may soon turn up for special projects like the one Thomas Struth did not long ago, inserting photographs among the paintings. And from the Casón del Buen Retiro, a museum annex some blocks away (Picasso’s “Guernica” was enshrined there behind glass for a time), the Prado’s 19th-century Spanish academic paintings, which almost nobody bothered to visit, have come home. They now occupy the new temporary exhibition galleries — a charming choice for a first show, because it’s hardly a crowd-pleaser. The show is meant as a statement about the untapped breadth of the collection. For a couple of hours the other day, the 19th-century paintings curators, giddy upon their liberation from years of exile in the Casón, sang to me the praises of artists like José de Madrazo, Vicente López, Eduardo Rosales and Fortuny. I was nearly convinced.Of course, most people will come for the classic collection, in the original building, which can finally be rationally reinstalled over the next couple of years. As Mr. Zugaza put it, “The real extension of the Prado is in the old building.” In the end, the beauty and dignity of the extension lie in this service to the art and tradition. Give much credit to Mr. Moneo, whose humility reflects a native’s respect for a national symbol and for the painters with whom he was wise not to compete. Subtlety is hard and self- effacement brave in this age of chest-thumping designers. The extension implicitly rebukes all the excessive posturing that has overtaken many museums lately. Perfect it’s not. But then, aside from Velázquez, what is?