The motions on behalf of attorney Paul Minor and Justice Oliver Diaz, Jr., were filed in U.S. District Court in Jackson.
U.S. Attorney Dunn Lampton says he will not comment on the motions.
Diaz and Minor, along with former judges Wes Teel and John Whitfield and Diaz's ex-wife Jennifer Diaz, are accused of participating in a scheme in which Minor allegedly provided cash, loans, and gifts to the judges in exchange for favorable decisions.
They were originally indicted last summer. A new indictment filed by federal prosecutors in February replaced the original case.
The new indictment charged Diaz and Minor with extortion besides fraud and bribery. All five have pleaded not guilty. A trial date has been set for Aug. 16.