It is harder than ever to get into a top-tier college. That was the message this week as several of the nation’s most selective universities trumpeted the news that they had record numbers of applicants — and record low admission rates.

But the news was also troubling for many parents and students in the wake of a vast cheating scandal, in which federal investigators charged dozens of parents this month in a scheme to buy their children’s way into college.

In some ways, the cutthroat admission rates — and the image of exclusivity that comes with them — point to why those parents, several of whom appeared in federal court in Boston today, were said to have bribed coaches and athletic directors to game an increasingly restrictive system.

“There’s a vicious cycle that fuels admission angst and spawns desperation,” said Sally Rubenstone, senior contributor to College Confidential, an online admissions forum. “Each year as elite-college acceptance rates get smaller, students apply to longer and longer lists of colleges to maximize their chances of good news.”

Several of the elite colleges named in court papers in the cheating scandal set admissions records this week. Yale’s admission rate sank to 5.91 percent from 6.31 percent last year, or 2,178 students out of a record-high pool of 36,843. The rate was 11 percent at the University of Southern California, the lowest ever, out of 66,000 freshman applications.

Colleges have a clear incentive to tamp down their admission rates, which figure in annual ranking surveys and help burnish schools’ sought-after status. At the same time, the plunging rates create more anxiety for students and parents as they weigh their higher education options.

Some schools have recognized that publicizing their admissions numbers helps fuel the madness of college admissions and have tried to pull back.

Last year, Stanford University, which is also mentioned in court documents in the scandal, announced that it would no longer release admissions data to the public, only to the federal government. Last year, its acceptance rate was 4.3 percent for the Class of 2022, below those of Harvard and Yale.

The rate at Harvard fell to 4.5 percent this year, down slightly from 4.6 percent last year. It also increased its share of Asian-American admits to 25.4 percent from 22.7 percent, at a time when it is waiting for a decision in a lawsuit accusing it of discriminating against Asian-American applicants.

Some parents said the record numbers reflected not more students applying, but the same students applying to more colleges. Pamela McCready-Huemer said her son and others who planned to take on popular majors like computer science and engineering had to hedge their bets.

“My son did apply to 20 schools, not for bragging rights, but because it’s so unpredictable, no one knows what will happen,” she said.

Admissions outcomes were even bleaker for the parents who arrived in a Boston federal courtroom today.

A lawyer for William McGlashan Jr., who appeared in court and is accused of arranging false test scores and conspiring to bribe a college official to get his son into USC, told the court this week that the son had withdrawn his college applications.

All of the parents were caught in recorded phone calls with the college consultant prosecutors say was at the center of the conspiracy, William Singer, who had become a government cooperator.

Some of the parents plan to fight the charges, and indicated in recent days they would argue that they were not in on Singer’s schemes, and that he was deceiving them, too.

A lawyer for Gamal Abdelaziz, a former casino executive, who is accused of conspiring to bribe an official to get his daughter into USC as a basketball recruit, said today that Abdelaziz believed he was making a legitimate donation to the university.

Lawyers for Amy and Gregory Colburn, a couple who have been accused of paying Singer to help their son cheat on the SAT, said this week that their clients knew nothing about any scheme to cheat.

“Their son took the test,” the lawyer, David Schumacher, said. “They had zero knowledge that anyone was doing anything with that test apart from their son taking it.”

As to why they donated $25,000 to Singer’s foundation — which prosecutors argue was a payment for the cheating scheme — another lawyer for the couple said that they believed it was a legitimate charity.

Neale Gay, a college guidance counselor in Massachusetts, said that students had started to be anxious about getting into college earlier and earlier.

“Gone are the days when the student just takes the SAT,” Gay said. “Their prestige, their name recognition, has created an incredibly competitive atmosphere for young people, and their increasing anxiety is really troublesome.”