A few selective, elitist universities may be announcing record numbers of applications for the semester this fall, but higher-education officials are fretting about ominous signs that overall college enrollment is decreasing.

More schools have space still available than any time in at least a decade. Many universities were offering greater discounts just to fill the seats in the last academic year. More than 40 percent of private colleges reported enrollment declines. Additionally, even community colleges experienced enrollment dips this year.

"We are seeing the beginnings of a cool down," Barmak Nassirian, associate executive director of the American Association of Collegiate Registrars and Admissions Officers, told Time.

The warning signs come at a time when policymakers from the president to governors are pushing to increase the proportion of the nation's population aged 25 to 34 with postsecondary credentials, which the Organisation for Economic Co-operation and Development says has already fallen from first to 16th in the world.

The cause of this decline in admissions, Nassirian says, is largely due to skyrocketing tuition and concern about debt.

States have cut the amount they spend on higher education, per student, by nearly 11 percent since 2010 to the lowest level since the 1980s, according to the State Higher Education Executive Officers organization, forcing the rest to be made up through higher tuition.

Already, at least 375 colleges report space still available for the fall, even at the end of the admission season, according to the National Association of College and University Business Officers.

The percentage of accepted students who actually enroll in any university or college, which is called the "yield rate," has fallen from about half to 41 percent in the last decade, NACAC says.

Schools pronouncements about record numbers of applications may be misleading because, with the ease of sending applications online, students are sending more than they did 10 years ago. So while there may be 33 percent more applications circulating, that doesn't necessarily translate into 33 percent more applicants.

Students confirm, loudly and clearly, that their college choices are more than ever being driven by price. In an annual survey of freshmen nationwide by the Higher Education Research Institute at UCLA, a record 42 percent said cost was "very important" in their decision about where to enroll. Record numbers also said financial aid was a factor for them-and was so essential that not being offered such help caused them to turn down the top schools on their lists.