Ms Barbagallo is opposed to witnesses being called to give their evidence-in-chief, and then "months later" being recalled to be cross-examined.
"Giving evidence in this trial for any witness is nerve-racking, it's heavily scrutinised, and this witness ought to be able to give his evidence and be cross-examined, in fairness to everybody," she said.
Mr Yovich has disagreed.
"I want to ensure the trial proceeds for no longer than it has to obviously, but my overriding concern is fairness to my client, and fairness to my client is to know what the evidence will be and have time to deal with it," he said.
In light of Mr Yovich's position, which Ms Barbagallo said she had not been made aware of until now, the prosecution has requested Mr Paton's evidence be deferred.
This application would also mean former Macro Taskforce boss Jim Stanbury's evidence would also be delayed.
Justice Hall has ordered a brief adjournment for the two parties to "have a chat" and work out how best to call the witnesses.