On Thursday, Federal Judge Kimba Wood appointed Jones, her former colleague, as a "special master." Jones is expected to determine which of the files, communications and electronics seized in the April 9 raids of Cohen's office and hotel room are protected by attorney-client privilege.
Jones brings with her extensive experience and qualifications for the job, but also some intriguing connections. Namely, she used to work under Rudy Giuliani when he was a U.S. attorney in Manhattan during the 1980s. The former New York City mayor and GOP presidential hopeful is now a member of Trump's legal team.
Yet it is exactly Jones' lengthy judicial career, and her diverse experience in law, that make her a prime choice for the role, according to Wood.
"In my view, the person best qualified to be special master in this case is Barbara Jones," Wood said.
Jones was selected by President Bill Clinton in 1995 as a judge in New York's Southern District, an appointment that came on the recommendation of late Sen. Daniel Patrick Moynihan, D-NY. She spent 17 years on the bench and presided over a wide array of cases, many of which involved questions of privilege.
Among her most famous cases involved Autumn Jackson, who was convicted in 1997 of attempting to extort millions of dollars from comedian Bill Cosby.
Cosby was convicted on three counts of aggravated sexual assault on Thursday — the same day Jones was appointed special master.
After she stepped down as a federal judge in early 2013, Jones acted as an arbitrator in the matter of National Football League running back Ray Rice, who had been suspended indefinitely after physically assaulting his fiancee in an elevator. Jones overturned his suspension.
In 2013, Jones made her first foray into private practice, joining the firm Zuckerman Spaeder. In the spring of 2016, she moved to become a partner at Bracewell, focusing on white collar issues. Jones joined Bracewell after Giuliani left his role as a name partner in the firm. Bracewell did not immediately respond to CNBC's request for comment on Jones' appointment.
She developed a particular expertise as an independent investigator in cases involving labor unions.
Over the course of her career, Jones cultivated a solid reputation, which was undiminished after Jones shifted to private practice. She received the Robert Morgenthau Award in 2016, an annual prize given to exemplary prosecutors, named after the famed New York district attorney.
"She is incredibly efficient," said Glen Kopp, a partner at Mayer Brown and a former colleague of Jones' at Bracewell. "She can consume, absorb and make sense of a lot of information very quickly."
Jones' ability to filter through the legal chaff will be tested in her new role as special master. She will be making determinations about the status of eight boxes' worth of hard-copy documents, and extractions from multiple cell phones, an iPad and other electronically stored files.
Kopp agreed with Wood that Jones is well-prepared for the task. She can "see through whatever is superfluous and unnecessary and get right down to it," Kopp said.
The question of who would review Cohen's seized materials has been a lingering point of contention in the court proceedings. Lawyers for both Trump and Cohen have argued that their clients should be the first to determine which of the documents are covered by attorney-client confidentiality, meaning they can't be turned over to the prosecutors investigating Cohen.
Prosecuting attorneys for the federal government have strongly opposed those arguments, and for weeks fought against the appointment of a special master. But they relented on the latter point in a recent court filing, prompting Wood to make the appointment.
Wood cleared some of the air in the Thursday hearing, rejecting the seven special master candidates suggested by the parties in the case, and installing her own hand-picked selection instead.
Once Wood settled the matter of who would review Cohen's seized materials, the attorneys launched a lengthy debate over the scope of Jones' authority.
The lead prosecutor, Tom McKay, said that Jones should only be evaluating whether or not the materials were covered by Cohen's claims of privilege. Stephen Ryan, a lawyer for Cohen, pushed to give Jones the power to determine if certain files, such as family medical records, were totally irrelevant to the matter at hand.
The two lawyers volleyed arguments back and forth for long enough that Joanna Hendon, a lawyer for Trump, at one point covered her face laughing in her seat.
Despite McKay's objection that giving the special master more powers would be a "very serious expansion of the scope" of the process that would "dramatically" slow it down, Wood appeared to grant Jones a small degree of leeway in the matter.