Parents including two US actresses accused in a college admissions scandal have been warned about broaching the case with their children.
A judge told defendants including Felicity Huffman and Lori Loughlin they should take care not to obstruct justice during family discussions.
They were among 13 wealthy parents who made their first appearances in Boston federal court on Wednesday.
Some 33 parents are charged in the investigation.
It is alleged they paid $25m (£19m) in bribes so their children could win spots in elite universities and conspired to cheat on college entrance exams.
On Wednesday, packaged food entrepreneur Peter Sartorio became the first to say he will plead guilty.
During the hearing, US Magistrate Judge M Page Kelley imposed conditions on all the defendants’ bail, ordering them to surrender their passports and not to have firearms in their homes.
Prosecutors had wanted the accused banned from discussing the charges with their children.
“The kids in these cases are witnesses and this could raise obstruction of justice issues,” prosecutor Eric Rosen argued in court.
But Judge Kelley said: “I just don’t think that’s realistic.”
She did, however, recommend the accused seek legal advice about any such family discussions so as to avoid the risk of interfering with the case.
Desperate Housewives star Ms Huffman, 56, did not speak as she left the court.
Lori Loughlin, 54, an actor in US sitcom Full House, signed autographs for fans outside court.