WASHINGTON (CNN) -- Vice President Dick Cheney's chief of staff and successor to Lewis "Scooter" Libby will resume his testimony Tuesday in Libby's high-profile trial, and is to be followed on the stand by former New York Times reporter Judith Miller.

While at the Times, Miller served 85 days in jail in 2005 for refusing to testify before the grand jury in the investigation of who leaked the name of CIA operative Valerie Plame Wilson.

David Addington, a prosecution witness, told CNN he expects to finish testifying Tuesday.

Addington came to the stand Monday and began to establish the process he used as Cheney's counsel in 2003 to respond to Justice Department requests for documents as the probe began.

After prosecutors finish their initial questioning, Addington will be cross-examined by Libby's defense lawyers. Prosecutors can ask follow-up questions. Following that, U.S. District Judge Reggie Walton can pose any questions from the jury, a process he has followed with previous witnesses.