The bitter fight between consulting giant McKinsey & Co. and retired restructuring adviser Jay Alix will get a “no-nonsense” mediator to help the parties get to the bottom of the conflict, U.S. Bankruptcy Judge Kevin Huennekens ordered in a court hearing Jan. 15.

The two bankruptcy cases in which Alix has accused McKinsey of hiding potential conflicts of interest will have “joint judicial mediation” with U.S. Bankruptcy Judge Marvin Isgur appointed as the mediator, Huennekens said.

“We need to get...