In 1986, following Chief Justice Warren Burger's confidential message to President Reagan that he planned to step down from the bench, White House Counsel Peter Wallison tasked a small team including Cox with thoroughly researching the opinions and judicial philosophies of the leading candidates for the next Supreme Court nomination. The effort focused on judges of the U.S. Court of Appeals who had a substantial record of decisions. After narrowing the field to five or six, the search quickly settled on Judge Antonin Scalia of the U.S. Court of Appeals for the D.C. Circuit, a recommendation the president accepted.