Museum leadership has become a kind of star system, in which a small group of directors can pull in seven-figure bonuses from boards eager to hang onto the talent.

Last year, the director of the Metropolitan Museum of Art, Philippe de Montebello, received a $3.25 million one-time payment as a reward for having stayed at the museum through his 70th birthday. His total compensation for the year was $4,557,342, making him the top earner in the Chronicle of Philanthropy’s annual survey of nonprofit executive compensation, beating out presidents of major hospitals and universities.

Other museum directors in Mr. de Montebello’s earning class include the director of the Museum of Modern Art, Glenn Lowry, who in addition to a compensation package that in 2004 was $1.28 million, between 1995 and 2003 received a total of $5.35 million from a trust set up by museum trustees. The former chairman, Robert Menschel, and president of MoMA, Marie-Josée Kravis, said in a letter to the New York Times that the trust helped to secure the recruitment of Mr. Lowry to the museum in 1995. In 2006, Mr. Lowry received $901,766 in compensation.

The other director who can bring in the big bucks is Peter Marzio, the head of the Museum of Fine Arts in Houston. In 2001, Mr. Marzio received a bonus of $1.7 million, on top of his $525,000 salary, as a reward for raising $237 million for an expansion and the museum’s endowment, instead of hiring outside development consultants. Last year, Mr. Marzio received compensation of $850,000.

Nonetheless, these three, as stars, are exceptions. Overall, while the median compensation of not-for-profit executives increased by 4.6% last year, it did not keep pace with the compensation of corporate executives, which increased by 6%. So it’s unlikely that ambitious college seniors will begin shunning offers from investment banks in order to work at not-for-profit arts organizations.

Many New Yorkers will likely think that Mr. de Montebello is worth every penny. “New York City’s incredibly lucky to have Philippe de Montebello,” the director of the Alliance for the Arts, Randall Bourscheidt, said. In addition to the respect Mr. de Montebello enjoys among his professional peers, “he’s become a popular figure,” Mr. Bourscheidt said.

The Chronicle of Philanthropy noted that nonprofit bonuses are increasing, following the trend in the corporate world of tying compensation to performance. Mr. Marzio’s compensation last year included a $400,000 bonus, and Mr. Lowry’s a $291,748 bonus.

But, as a museum headhunter at Russell Reynolds Associates, Malcolm MacKay, observed, the logic behind structuring bonuses is not nearly as clear in the cultural world as in corporate one, since it is difficult to define a cultural organization’s fulfillment of its mission in purely quantitative terms. Attendance, for instance, is easy to quantify, but “what if you do something that is not appropriate [to the mission] but brings in a lot of people?” Mr. MacKay asked.

On another side, if a bonus is tied to fundraising, it means that when the director asks someone for money, he “is benefiting directly himself,” Mr. MacKay noted. “Is that something you want to encourage? How does the donor feel about that? These are all difficult questions,” he said.

Indeed, these and similar questions have led to increased scrutiny of nonprofit executive pay. The former president of the J. Paul Getty Trust, Barry Munitz — who is listed on the survey as being compensated with $898,361 in fiscal year 2006 — resigned in February 2006, in the midst of an investigation by the California attorney general into his compensation and spending practices. Critics asserted that he mingled his own and the Getty’s interests, by approving grants for friends, spending Getty funds on first-class international travel with his wife, and lobbying for raises while ordering budget cuts and layoffs. On his resignation, Mr. Munitz repaid $250,000 to the Getty.

More recently, the former secretary of the Smithsonian Institution, Lawrence Small (who earned $587,742 according to the survey) and the chief executive of the Smithsonian’s business unit, Gary Beer (who earned $498,964), gave up their jobs in the wake of scandals involving expenditures.

And the pressure for cultural institutions to justify their compensation practices is likely only to increase, since Senator Grassley, a Republican from Iowa, and a ranking member of the Senate Finance Committee, has made it his personal mission to crack down on not-for-profits that he sees as abusing their status and serving as tax write-offs for the wealthy. What this will mean for the museum star system is yet to be seen, but Mr. MacKay suggested that cultural not-for-profits could afford to devote more thought to their compensation practices.

“More work has to be done in terms of figuring out how to structure [things like bonuses] in a way that is productive for everybody,” he said.

Perhaps the most remarkable compensation at a cultural organization listed in the survey is that of Dennis O’Connell, a stagehand at Carnegie Hall who last year earned $383,044 — $150,000 more, for example, than did the director of the Philadelphia Museum of Art, Anne d’Harnoncourt. A spokeswoman for Carnegie Hall, Synneve Carlino, said that Mr. O’Connell is paid in accordance with Carnegie Hall’s labor contract with the International Alliance of Theatrical Stage Employees/Local One.