The University of Virginia’s top leaders discussed the school’s finances for more than three hours Wednesday afternoon, returning again and again to one question: Should they continue to increase tuition each year?

A string of administrators told members of the U-Va. Board of Visitors that more money is needed to keep up with costs mandated by the state, such as retirement benefits and salary increases, and to improve the quality of an undergraduate education. One idea the administration has proposed is to charge third- and fourth-year students an annual $2,000 “Academic Excellence Fee” to cover the higher cost of smaller classes, personalized advising and other perks.

“As the father of a second-year . . . I would be thrilled, frankly, if I had the opportunity to pay a bit more, whether it’s tuition or fees, to provide the smaller classes and better advising,” among other things, said Carl P. Zeithaml, dean of the university’s McIntire School of Commerce, which charges its students a higher tuition rate to cover its higher expenses. “The quality of that experience will benefit these students for a lifetime, not just for the first job.”

While most board members quietly listened or took notes, a few openly questioned the need for a tuition increase, especially one that seems hidden in a fee. In the past decade, the in-state tuition rate at U-Va. has nearly doubled, far outpacing the rate of inflation. Looking over balance sheets showing the flow of millions and millions of dollars, they asked if a tuition increase was merited. They also questioned an administration proposal to cut 1 percent of costs and redirect that funding toward innovative new programs. One member suggested cuts of 3 to 4 percent, and others suggested that the savings could help offset the need to charge students more for tuition.

“I haven’t seen or heard how we are going to do things differently to save money,” said Helen E. Dragas, leader of the governing board. “We all want to be like a private [university]. We all want to charge as much as we can and deliver the best that we can. But that’s not what we are,” she added.

See the University of Virginia draft report.

Wednesday’s discussion foreshadows two meetings. Later this month, the board is scheduled to set tuition for next year. And in May, the board is set to review and approve U-Va. President Teresa A. Sullivan’s budget for the coming fiscal year.