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NEW YORK – Enrollment at American colleges is sliding, but competition for spots at top universities is more cutthroat and anxiety-inducing than ever. In the just-completed admissions season, Stanford University accepted only 5 percent of applicants, an all-time low among the most prestigious schools, with the odds nearly as bad as those at its elite rivals.

Deluged by more applications than ever, the most selective colleges are, inevitably, rejecting a vast majority, including legions of students they once would have accepted. Admissions directors at these institutions say that most of the students they turn down are such strong candidates that many are indistinguishable from those who get in.

Bruce J. Poch, a former admissions dean at Pomona College in Claremont, Calif., said he saw “the opposite of a virtuous cycle at work” in admissions. “Kids see that the admit rates are brutal and dropping, and it looks more like a crapshoot,” he said. “So they send more apps, which forces the colleges to lower their admit rates, which spurs the kids next year to send even more apps.”

For most of the last six decades, overall enrollment boomed, while the number of seats at elite colleges and universities grew much more slowly, making them steadily more selective.

Enrollment peaked in 2011, and it has dropped a bit each year since then, prompting speculation that entry to competitive colleges would become marginally easier. Instead, counselors and admissions officers say, the pool of high-achieving applicants continues to grow, fed partly by a rising number from overseas.

At the same time, students send more applications than they once did, abetted by the electronic forms that have become nearly universal, and uniform applications that can make adding one more college to the list just a matter of a mouse click.

A generation ago, it was rare for even highly competitive colleges to offer places to fewer than 20 percent of their applicants. In 2003, Harvard and Princeton drew exclamations of dismay (from prospective applicants), envy (from other colleges) and satisfaction (from those they accepted) when they became the first top universities to have their admission rates dip below 10 percent. Since then, at least a dozen have gone below that threshold.

Richard H. Shaw, dean of undergraduate admission at Stanford, said he could not predict where the rates would bottom out – in fact, he never expected them to go as low as they have.

“Honestly,” he said, “I’m sort of in shock.”

Some officials also pointed to colleges’ increasingly aggressive outreach to prospective students, with mailings, emails and advertising – some of it well intentioned, and some of it more cynical.

“One of the ways that colleges are measured is by the number of applicants and their admit rate, and some colleges do things simply to increase their applicant pool and manipulate those numbers,” said Christoph Guttentag, dean of undergraduate admission at Duke.