Officials at many of those schools that beat the odds say they dug more deeply into their applicant pools, recruited aggressively and kept the cost to families as low as they could. Schools in the survey of private colleges increased institutional aid by 9% — more than twice the average tuition increase, 4.3%, the smallest average annual increase since 1972-73.

And it worked, even for some of the most affluent families, says Lisa Jacobson, founder of Inspirica, a 26-year-old tutoring company based in New York. Families that in past years may have considered only schools ranked at the top of U.S. News & World Report’s best-colleges list also applied to a few state schools this year — “just in case,” she says.

But “what was fascinating was there was so much merit money out there this year” among private colleges, particularly those a little farther down in the rankings. The students “were so flattered and the parents were so happy.”