Burns said he made the mistake in trying to accommodate concerns from Loughner's attorneys about the impartiality of the Bureau of Prisons professionals conducting the exam.
The judge still approves of having a second exam but now proposes appointing a psychiatrist who has no affiliation with the Bureau of Prisons to conduct it, rather than letting Loughner's attorneys chose the professional.
Burns said his proposed changes would eliminate any distinction between a court-ordered exam and one done by a psychiatrist picked by the defense. "Instead, there would be two court-ordered examinations," Burns wrote.
A final decision on the matter will be made by the 9th U.S. Circuit Court of Appeals.
Burns proposed his changes to the mental exam order after Loughner's attorneys appealed his ruling to the 9th Circuit and judges on the appeals court asked Burns to chime in.
The appeals court rejected a request last week by Loughner's attorneys to put the exam on hold and return him to Arizona. But the court temporarily put on hold Burns' requirement that video recordings of Loughner's exam be provided to both prosecutors and defense attorneys. The exam will still be video-recorded, but the recordings will be set aside as lawyers litigate the issue.
Loughner has pleaded not guilty to dozens of federal charges stemming from the Jan. 8 shooting at a meet-and-greet political event. U.S. Rep. Gabrielle Giffords and 12 others were wounded in the attack, and six people were killed, including a 9-year-old girl and a federal judge.
The charges against Loughner include trying to assassinate Giffords, as well as murder in the deaths of U.S. District Judge John Roll and Giffords aide Gabe Zimmerman.
Giffords remains at a rehabilitation center in Houston as she recovers from a bullet wound to the brain.