Earlier this year, attending a public university seemed like a no-brainer for Nicole Barker. The aspiring Egyptologist from Evanston, Ill., had gotten into the University of Illinois -- and her top private choice, Bryn Mawr, had a sticker price of $56,000 a year. But Bryn Mawr counterpunched, offering almost $29,000 a year in loan-free aid. That made the total cost comparable with what Illinois charged -- even at in-state rates. "We were surprised, and thrilled," says Nicole's mother, Danielle Schultz.

Thrills like these may soon become less surprising. The tuition gap between public and private colleges has narrowed, with public tuition rising about 120 percent in the past decade, almost twice as fast as private. And with more families balking at the price, some private schools are now dipping into their endowments to lure top students away from state-school competition. (Illinois says its admitted students often see competing offers from "well-endowed private schools.") For many families, says Lynn O'Shaughnessy, the author of "The College Solution," the assumption that state schools are always cheaper is "just not true."

Such bidding wars aren't entirely new: A few Ivy League schools have offered "no loan" aid for middle-income families for several years. But observers say the generosity is now quite pronounced at smaller liberal arts schools, whose Ivy-like prices don't necessarily confer top-tier salary clout on the job market. Jenny Rickard, Bryn Mawr's chief enrollment officer, says 69 percent of the student body got grant-based aid in 2011, averaging just under $30,000 per student. Public schools can seldom make similar offers, because they have to cope with state budget cuts. At the University of Michigan, out-of-state tuition now tops $30,000 a year, and the school says per-student aid from the state has shrunk more than 50 percent over the past decade.

Still, even at the most generous private schools, 30 to 40 percent of students get no aid at all. So what kind of factors can work in a student's favor? Experts advise families to track down schools that award a lot of "merit aid" -- the nonprofit College Board has a Web database of such stats. Students should also aim for schools where their grades and test scores fall into the top 25 percent of the applicant pool, says Deborah Fox, a San Diego financial planner specializing in planning for college. After all, says Fox, "the most highly desirable students get the best packages."