Officials at the College Board said students who needed double the time or more to take the test would now be required to take it at their home schools, with rare exceptions.

According to court papers in the admissions case, the mastermind of the cheating scandal, William Singer, knew that if students were able to double their testing time by claiming they had a disability, they could also request testing sites of their choice, sometimes thousands of miles away, where Mr. Singer would arrange for cheating.

The College Board said it was now cracking down on such site arrangements. Any cases in which students request to take tests at schools other than their own “will require verifiable justification and implement additional enhanced security processes,” Jerome White, a spokesman for the testing company, said.

Guidelines for those exceptions were still being developed, Mr. White said.

[Read: Is the college cheating scandal the “final straw” for standardized tests?]

But the College Board said on Friday that it did not plan to change how it grants extra-time accommodations, and defended its process as “thoughtful and balanced.” Most students who receive special allowances for tests at school “automatically” get them for standardized tests as well, the company said, although it does employ its own clinicians who may review and overrule requests in a small number of cases.

The company played down the significance of the admissions scandal for the testing industry. Officials said it had involved a tiny number of cheating allegations over eight years, compared with the millions of SAT tests taken over the same time. Similarly, they said, the case pointed to two corrupt proctors out of tens of thousands around the world.

“Let’s be honest, this is not a kid looking over their shoulder at another kid’s answer sheet,” Mr. Schwartz said. “You’ve got to get a grown-up to jeopardize their job, their future and their freedom, because these are crimes that somebody’s going to jail for. That is really hard and really rare.”