“For example, publicity will forewarn probable future John Doe witnesses of the State’s interest in questioning them. Such warning may result in statements that are less likely to be entirely candid,” he said. “Publicity arising from a public John Doe proceeding may also make it more likely that evidentiary records will be lost or destroyed before being subpoenaed.”

In his petition, Nelson argued that the “formality” of a John Doe would “increase the likelihood of complete and frank statements by persons who otherwise may profess a failed or an incomplete recollection to an investigating law enforcement officer in an informal interview setting.”

The John Doe investigation was halted last month when U.S. District Judge Rudolph Randa sided with O’Keefe and his group in a lawsuit they had filed and issued a preliminary injunction, saying their First Amendment rights had been violated.

Prosecutors have appealed his ruling. And on Wednesday, they filed briefs in the 7th U.S. District Court of Appeals arguing for a stay that would put Randa’s ruling on hold.

In their filing, prosecutors also said O’Keefe and Wisconsin Club for Growth misunderstood their jurisdictional limits and took issue with O’Keefe’s description of “raids” on targets’ homes.