Early-admission applications to some of the nation’s most selective colleges remained near historic highs this year, as the admissions process for those institutions continues to shift into high gear earlier and grow more uncertain for applicants and schools.

Applications for binding early decision or more flexible early action programs jumped last year at schools including Harvard University and Brown University as anxious high-school seniors embarked on a chaotic admissions cycle. Schools ditched testing requirements, placed campus visits on hold because of the pandemic and are still sorting through whether students who deferred enrollment from the prior year would take away spots from the coming class.

This fall, early decision applications declined at the University of Pennsylvania, Dartmouth College and Columbia University from fall 2020, but remained far higher than the volume reported in other recent years.

Columbia received 6,305 early-decision applications this year, a 2% drop from 2020 but a figure that still tops the prior record by more than 40%. Applications to Dartmouth were off by 1%, and at Penn they declined by 2%.

Brown reported an 11% increase in early-decision applications, citing the expansion of its financial aid program as a likely factor in the heightened interest.

At Yale University, the number of applicants who sought entry under a restrictive early-action program edged slightly lower from last year but topped 2019 figures. The school doesn’t let candidates submit applications to other private colleges in the early-admission round, but does allow them to apply elsewhere in the regular application cycle and doesn’t require them to commit until the spring.

Yale admitted 11% of the 7,288 students who applied early.

Harvard admitted 7.9% of its 9,406 early-action applicants, a slightly higher admit rate and lower applicant count than last year. The school said it would extend its test-optional policy for at least the next four years, because the pandemic continues to make it difficult for some students to find testing sites.

Hundreds of other colleges have already said they would remain test-optional for at least another year or two, with some permanently ditching testing requirements altogether. About 80% of undergraduate programs aren’t requiring SAT or ACT scores for the current crop of high-school seniors, according to FairTest, a nonprofit that urges more limited use of standardized tests. Harvard’s announcement could set off a wave of similar statements from peer schools who compete for the same candidates.

Meanwhile, Princeton University said Thursday evening it would no longer release application or acceptance figures for the early or regular admission cycles.

“We know this information raises the anxiety level of prospective students and their families and, unfortunately, may discourage some prospective students from applying,” the school said in a statement posted on its admissions website.

Stanford University in 2018 stopped reporting that data, saying at the time it wanted to de-emphasize the perceived value of low acceptance rates. Cornell University has said it would no longer release such detailed figures either.

Candidates who apply in early admission rounds generally have a much higher shot of getting in than those who submit applications during the regular decision cycle.

Early-round applications tend to come from the wealthiest students, as those candidates may attend high schools with more robust college counseling services and might not need to compare financial aid offers. About 60% of students who submitted the Common Application through Nov. 16 lived in the most affluent 20% of ZIP Codes nationwide, the group reported. Applicants from the bottom quintile made up 5% of the applicant pool through mid-November.

Because applicants are each submitting more applications than they did even a few years ago, it has become harder for schools to predict which admitted students will enroll, a metric known as the yield. If a school accepts too many students, it could run out of housing and classroom space. Too few, and it might not meet revenue targets.

The institutions have increasingly sought predictability by locking in a large share of their incoming students through binding admission decisions, and it isn’t uncommon for even the most selective schools to fill half their first-year class with early commits.