Lawyers for the federal government clashed with lawyers for a group of California scientists at the U.S. Supreme Court on Tuesday over how much information the government can demand in background checks on potential employees before violating their privacy rights.

And the justices themselves appeared to have conflicting concerns about background investigations. “Are there any limits on what the government can ask?” Justice Sonia Sotomayor pressed Acting Solicitor General Neal Katyal shortly after he opened his argument in National Aeronautics and Space Administration v. Nelson. Can the government ask someone about his genetic makeup because “we don’t want someone prone to cancer?” she added.