David Kris, who ran the Justice Department’s National Security Division early in the Obama administration and helped write a book about FISA, says that when the department submits material from sources to the court, “it should also include information that would cast material doubt on their credibility — sources often come with bias or baggage of one sort or another.”

But, he said, “there is no requirement for elaborate accounting: Courts routinely accept and uphold affidavits that generally describe a source’s shortcomings” without every specific detail.

William C. Banks, a Syracuse University law professor who has studied the FISA Court, said that without reviewing all the documents involved in the surveillance request, it was impossible to judge the importance of how Mr. Steele was described. But he emphasized that the government had broad leeway in seeking FISA warrants.

“Carter Page was doing business in Russia, talking to Russian diplomats who may have been involved in intelligence activities directed at the United States,” Mr. Banks said. “Game over. The standards are incredibly open-ended.”