The judge in Donald Trump’s hush money trial ordered the media on Thursday not to report on where potential jurors have worked and to be careful about revealing information about those who will sit in judgment of the former president.

Judge Juan Merchan acted after one juror was dismissed when she expressed concerns about participating in the trial after details about her became publicly known.

The names of the jurors are supposed to be a secret, but the dismissed juror told Merchan she had friends, colleagues and family members contacting her to ask whether she was on the case. “I don’t believe at this point I can be fair and unbiased and let the outside influences not affect my decision-making in the courtroom,” she said.

Merchan then directed journalists present in the courthouse not to report it when potential jurors told the court their specific workplaces, past or present. That put journalists in the difficult position of not reporting something they heard in open court.

Some media organizations were considering whether to protest having that onus placed on them. Generally, the First Amendment of the U.S. Constitution bars judges from ordering journalists not to disclose what they hear and see in courtrooms open to the public, though there are exceptions, such as when military security is at stake.

New York criminal defense lawyer Ron Kuby said that while judges typically can’t control what the media reports, other options are available to protect juror anonymity, including restricting what reporters see and hear in the courtroom.

“There are actions the judge could take,” he said. “Courts have extraordinary powers to protect jurors from tampering and intimidation. It is really where a court’s power is at its peak.”

The court action underscored the difficulty of trying to maintain anonymity for jurors in a case that has sparked wide interest and heated opinions, while lawyers need to sift through as much information as possible in a public courtroom to determine who to choose.

Despite the setback, 12 jurors were seated by the end of Thursday for the historic trial. Trump is charged with falsifying his company’s business records to cover up an effort during the 2016 presidential election campaign to squash negative publicity about alleged marital infidelity. Part of the case involves a $130,000 payment made to porn actor Stormy Daniels to prevent her from making public her claims of a sexual meeting with Trump years earlier. Trump has denied the encounter.

New York state law requires trial attorneys to get the names of jurors, but the judge has ordered the lawyers in Trump’s case not to disclose those names publicly. The jurors’ names haven’t been mentioned in court during three days of jury selection.

Still, enough personal information about the jurors was revealed in court that people might be able to identify them anyway.

Some news organizations described details including what Manhattan neighborhoods potential jurors lived in, what they did for a living, what academic degrees they had earned, how many children they had, what countries they grew up in and what their spouses did for a living.

On Fox News Channel Wednesday night, host Jesse Watters did a segment with a jury consultant, revealing details about people who had been seated on the jury and questioning whether some were “stealth liberals” who would be out to convict Trump.