UNC-Chapel Hill trustees might be on a collision course with the systemwide UNC Board of Governors — and perhaps the General Assembly — over whether the Chapel Hill campus will expand enrollment significantly.

Such a potential conflict became evident at the last trustees meeting on Sept. 25. At the meeting, unlike a Board of Governors meeting, there was little discussion about providing greater access to higher education. The subject was how UNC-Chapel Hill can persuade more top North Carolina high school students, as measured by SATs and class standing, to attend UNC-Chapel Hill.

As Chancellor Holden Thorp said at the beginning of the meeting, the goal of UNC-Chapel Hill is to give “the smartest students in North Carolina the best education.” UNC-Chapel Hill’s reputation depends heavily on the quality of its students.

Trustees are feeling pressure from the Board of Governors and the state legislature for UNC to “do its fair share” in finding places for 80,000 additional students anticipated over the next 10 years. It appears the boards already are chafing under the legislature-imposed 18 percent limit on out-of-state students.

Out-of-state students tend to be highly qualified, and if UNC-Chapel Hill could recruit more out-of-state students university officials would have an easier time maintaining the quality of the student body. Because few students can come from outside North Carolina, the motivation is intense to get as many of the most accomplished in-state students as possible to Chapel Hill.

Under the current rules, if UNC expands enrollment, it will almost inevitably bring in less-qualified students. As a consultant to the university pointed out to the trustees, the quality of the student body is an important part of UNC-Chapel Hill’s reputation. If prospective students begin to think that the school is becoming less prestigious, their perception could “compound the negative effect” of expansion itself.

The university already is in an increasingly competitive environment as it recruits top students, said Stephen Farmer, director of the Office of Undergraduate Admissions. In a detailed presentation on the entering freshman class, he said that the applicant “yield” went down this year by three percentage points. That is, the number of applicants accepted by UNC-CH who actually enrolled was 52.9 percent, compared with 55.7 percent last year and 54.6 percent five years ago.

UNC’s quality academic environment has brought it into direct competition with the South’s pre-eminent colleges and universities for those much-sought-after students who score 1,400 or higher on the math and verbal portions of the SAT, Farmer said. These schools include Duke, Wake Forest, Davidson, Virginia, Vanderbilt, and Washington University in St. Louis.

“We’ve played ourselves into a higher league,” he said.

Much of Farmer’s presentation was positive. This is the third straight year in which the number of applications, 21,507, set a record. Thirty-four percent were accepted, and this “admit rate,” a measure of selectivity that contributes importantly to the U.S. News rankings, is the lowest ever. But the decline in yield also can be seen as a warning bell for university officials and trustees.

Richard Hesel of the consulting firm Art and Science Group, LLC, reported on his firm’s polls of prospective Chapel Hill students. He said that “when tested simply as a number,” an increase to 33,000 students, from 27,700 now, would not have a significant impact on applications or enrollment — but only if student quality remains as high as it is now. He measures student quality as the percentage of UNC-CH students in the top 10 percent of their high school class. For freshmen entering this year, the figure is 79.1 percent. Growth to 36,000 would have a negative impact, regardless of its impact on quality.

Prospective students perceive UNC-Chapel Hill as a big campus, Hesel said. The leading reason given by accepted students who do not enroll is that the university is “too big.”

But high school students’ perceptions of academic quality and the highly selective student body “are often favorable enough to overcome the negatives they associate with size,” Hesel said. It is essential to maintain this selectivity by tying growth targets to “achievement of student quality measures.”

Hesel recommended that the university take a number of steps to bolster recruitment of the top N.C. high school students. His top recommendation was to use more merit-based aid. Merit aid is a grant that is not based on a student’s financial need but on a student’s aptitude and accomplishments. Hesel’s study estimated that a $2,500 increase in merit aid per student would raise acceptances from “top North Carolinians” by 8 percent. A $5,000 increase would increase them by 17 percent.

Chapel Hill already grants some merit aid. This includes named scholarships such as the prestigious Morehead-Cain and Robertson awards, which offer opportunities such as education abroad in addition to full funding. But even the news on these scholarships was not the cheeriest: Acceptances of the Morehead scholarships were lower this year.

An animated conversation by board members indicated that the issue of enrollment growth will not be settled quickly.

Jane S. Shaw is president of the John W. Pope Center for Higher Education Policy in Raleigh.