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Officials then had to “go through the additional legal process” to get the name of the phone subscriber, ensure that there was “predication,” meaning sufficient grounds to open a full federal investigation, and obtain a warrant for a wiretap.

On the basis of that surveillance, four men were convicted this year of fundraising for al-Shabab.

“That is one case where you have [Section] 215 [data-gathering authority] standing by itself,” Mr. Mueller told Senate Judiciary Committee Chairman Patrick J. Leahy, Vermont Democrat.

But Mr. Wyden and Mr. Udall, the two Democrats who have seen classified information about the cases, said Mr. Mueller and other officials were giving credit to Section 215 domestic collection for foiling plots that actually were thwarted using foreign intelligence programs such as Section 702.

“Saying that ‘these programs’ have disrupted ‘dozens of potential terrorist plots’ is misleading if the bulk [domestic] phone records collection program is actually providing little or no unique value,” they said in their statement.

In fact, the ACLU’s Mr. German said, the huge proliferation of electronic surveillance data was overwhelming the FBI and “just making the haystack bigger.”

He noted as an example of missing a needle that the FBI’s Webster Commission Report into the bureau’s failure to identify accused Fort Hood shooter Maj. Nidal Hasan as a jihadist called the case “a stark example of the impact of the data explosion.”

“The exponential growth in the amount of electronically stored information is a critical challenge to the FBI,” the commission concluded.

Also Thursday, the FBI acknowledged that Deputy Director Sean Joyce misspoke this week in describing to lawmakers details about another of those four cases, involving a Kansas City man called Khalid Ouazzini.

Mr. Ouazzini was placed under court-ordered surveillance by the FBI after the NSA discovered he had been in email contact with a terrorist suspect in Yemen, Mr. Joyce said. He added that the surveillance uncovered a “nascent” plot to bomb the New York Stock Exchange.

“Was the plot serious?” he was asked.

“I think the jury considered it serious, since they were all convicted,” he replied.

But an FBI official acknowledged Thursday that Mr. Ouazzini and two associates in New York had merely pleaded guilty to lesser charges of money laundering or providing support to terrorist groups.

Nevertheless, the official defended that case as an example of the program’s success regardless of the specific convictions ultimately achieved.

“We stand behind the example that was provided,” he said.

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