Yet the pace of construction continues. "I'm on the Cincinnati Art Museum board, among others, and I don't know anyone who's not expanding," says Lois Rosenthal, who with her husband, Richard, donated the naming gift for Zaha Hadid's $34 million Contemporary Arts Center, which opened in Cincinnati in 2003. "It's pretty frightening. I don't know where all the money is that's going to pay for it."

Adrian Ellis, chief executive of AEA Consulting, a New York- and London-based firm that advises cultural institutions, agrees that there's "no tailing off" in expansions. But he sees the funding problem differently: There's too much, not too little. An overabundance of available money is driving the spending spree, says Ellis, and a lot of wealthy people are keen to have their names on wings, galleries, or walls of a museum designed by a world-famous architect. In Atlanta, for example, F. Terry Stent, the trustee who headed the capital campaign for the High's $109 million expansion, had no problem raising money. "We got so few noes it was amazing," he says. "People wanted to catch the train before it was gone." In Milwaukee, says trustee Donald Baumgarten, the museum actually added features to its growth plans because it reached its initial goal of $100 million so quickly.

Museums, in other words, are expanding because they can.

To be fair, many institutions have been forced to build because of space constraints. Others, like the old High, had structural issues. Its 1983 Richard Meier-designed home, which had one elevator that held 12 people and limited gallery space, couldn't handle big shows. Neither could Denver's original 1971 building, designed by Milanese modernist Gio Ponti. Collections have grown exponentially at too many museums to mention. The Los Angeles County Museum of Art, which is in the midst of a multiphase expansion project, needed to reorganize its sprawling campus. The scale of many contemporary works, a category everyone is anxious to collect, has increased as well.

But it's also no secret that patrons are far more likely to write checks for construction than for anything else—especially now that museum building has become a competitive sport among cities. Not surprisingly, capital campaigns that aren't organized around a large building project face serious hurdles. What about buying art—maybe a trophy piece, like Gustav Klimt's 1907 portrait Adele Bloch-Bauer I, purchased by Ronald Lauder last June for the Neue Galerie, in New York? That alternative, trustees everywhere confirm, never comes up in the boardroom, where construction is the subject at the top of everyone's agenda.

"Most museum directors know better," says Nelson-Atkins head Wilson, who has kept projections of visitor numbers for his museum's expansion modest. "They get pushed into it by the trustees." As a result, Ellis adds, "a lot of museum directors are in a sort of quiet pain."

One recent day, the Hamilton wing in Denver is comfortably full of people. They stare up at its latticed atrium and roam galleries filled with temporary exhibitions of cutting-edge works, classic Japanese scrolls, and contemporary Native American pieces. Some visit the permanent collections of Western and contemporary art in their new homes. In Atlanta, the High is even more crowded, perhaps because school groups seem to be everywhere. Many are there to see "Kings as Collectors," a big loan show from the Louvre that fills the new Anne Cox Chambers wing.

But it's hard to miss another phenomenon at both places: The old buildings are pretty empty. That's why directors are sweating. With every addition comes a crush of visitors. But an inevitable diminuendo follows that crescendo. After the Museum of Fine Arts in Houston added an expansion, designed by Rafael Moneo, in 2000, attendance jumped to almost 1.8 million; in 2005 the figure was not quite 1.3 million. In Milwaukee the number of visitors climbed to more than 500,000 before falling back to less than 300,000. The Fort Worth Museum of Modern Art drew 300,000 in 2003, the year it opened its brand-new Tadao Ando building, versus 185,000 in 2005. At the Peabody Essex, attendance zoomed to 237,000 in 2004, then dropped by 40,000 the next year (it has since climbed back to 247,000).