Yale’s financial-aid overhaul seems to be receiving a favorable reception from high-school students and their college counselors, but the details of the plan — obsessed over for weeks by its crafters — are still unclear to many of them.

Interviews with counselors and high-school students from public and private schools on both coasts suggest that while potential Eli applicants are largely applauding the new policy, many know little more than that an aid announcement was made.

But debate still exists in high schools over whether the bold policies announced by Yale and Harvard over the past several weeks will actually have a negative influence on the aid packages students receive from smaller, less-wealthy institutions — something that could affect the majority of high-school students.

The effect of positive media attention on financial aid will be most felt a few months down the road as students begin to consider schools previously ruled out because of cost, said Jonathan Shea, director of student services at the public Woodrow Wilson High School in Washington, D.C.

“The largest effect will be in the future, with students looking at these institutions and saying they can get in,” Shea explained, “and it’s now possible to go there because of the finances.”

Yale’s aid initiative, announced Monday, reduces the expected contribution from families with annual incomes up to $200,000, eliminates the need for student loans and reduces the annual student contribution, among other measures. The plan will increase the University’s financial-aid budget from $62 million to $86 million, an increase of nearly 40 percent.

The new policy shares many features with the financial-aid plan unveiled by Harvard in a surprise December announcement.

Some of the guidance counselors and students interviewed said even broad knowledge of the new policy could tip the matriculation decisions of students with financial worries in favor of Yale.

Elyse Artin, college counselor at the public John F. Kennedy High School in Los Angeles, said several of her middle-class students had turned down Ivy League schools in the past because the financial aid was insufficient. The new policies at Harvard and Yale will change that, she said.

In one case, she said, a student was accepted to Harvard but chose to attend the University of California, Berkeley, because he has two younger siblings and his parents — both college graduates in the middle-income bracket — could not afford the tuition.

“Those students who are accepted at exclusive schools, unless they get an excellent financial-aid package, have gone to UC campuses,” Artin said.

Yale’s new aid policy could increase its yield among middle-income students, based from interviews with several applicants to Yale’s class of 2012.

Misha Lemesh, a senior at the private Deerfield Academy in Massachusetts who applied to both Yale and Harvard regular decision, called financial aid “the single most important factor” in choosing where to apply.

Lemesh, who is from the Ukraine, said he is leaning toward Yale right now, should he be accepted. But he said his decision might have been affected had Yale not followed Harvard’s lead on financial aid.

As part of the new initiative, Yale has promised to put an online calculator on its financial-aid Web site to help students estimate their financial-aid packages. The calculator will be functional sometime this summer, Dean of Undergraduate Admissions Jeff Brenzel said.

Many of the high-school students and guidance counselors interviewed said they expected Yale to match Harvard’s new policy and would have been shocked had the school come up with a lesser plan.

“This move definitely keeps Yale very much in the competition,” Deerfield Academy Director of College Advising Martha Lyman said. Without a commensurate offer, she said, Yale would have lost students to Harvard and other schools with stepped-up financial-aid packages.

Some Yale applicants never questioned that the University would meet the new status quo.

“I was certain that Yale would respond with a better financial-aid plan,” said Clark Xue, a senior at Mark Keppel High School in Alhambra, Calif.

Xue, who was accepted early to Yale but has applied regular decision to Harvard, said he will still compare the two schools’ financial-aid offers but will now put more emphasis on other more qualitative factors in his decision, such as size and location.

Yale’s announcement has ramifications that go beyond New Haven, several guidance counselors said.

The increased competition for talented middle-income students may encourage less selective institutions to offer more merit aid as opposed to need-based aid, Shea said.

While Yale has the resources to subsidize the tuitions for lower-income as well as middle-income students, he said, many other schools do not, which could impact the neediest students at these schools by reducing the amount of aid available to them.

The amount of need-based aid at these schools could be reduced because smaller schools will have to offer more merit-based aid in order to attract the best students.

But Kevin Newman, associate director of college counseling at the private Brentwood School in Los Angeles, said he does not think there will be a “trickle-down” effect.

Yale, Harvard and other highly selective institutions accept applicants from a relatively small pool of highly successful students, Newman said.

As a result, he explained, the wave of financial-aid reforms will affect only the small group of universities who compete for these students.

Although one of the new aid policy’s selling points is its clarity, some students are still in the dark.

Julie Zhu — a senior at the public Montgomery Blair High School in Maryland who was accepted early to Yale — said she is unsure how the financial-aid office will treat the separate incomes of her parents, who are divorced.

“I’ve tried to find out what happens when a kid’s parents are divorced,” Zhu said. “The Web site says they deal with it on a case-by-case basis, and I was a little confused by that.”

Director of Student Financial Services Caesar Storlazzi said the office takes information from both biological parents into account and calculates an expected contribution for each parent.

But Brenzel said while he appreciates the benefits of the media coverage Yale has received — and its potential effects on the applicant pool — he expects serious candidates for Yale will be able to find the relevant information on their own.

“The people we care about most are the admitted students, and the admitted students will get the news on their bottom line,” Brenzel said, referring to their tuition bills. “It’s delivered right to their door.”