Underworld figure George Alex has been excused from appearing before the Royal Commission into Trade Union Governance and Corruption on Friday, but will be called to appear on October 23.
Mr Alex had been summonsed to appear on Friday to give evidence about allegations that his labour-hire businesses made a weekly payment of $2500 to the national construction union.
The CFMEU has denied it received any kickbacks from Mr Alex.
Mr Alex's solicitor John Hajje made a submission to prevent Mr Alex's doctor, Jeremy Cumpston, from giving evidence in public on the basis that it would reveal personal details of a health condition.
He also made an application for Mr Alex to be excused from giving any evidence as scheduled on Friday.
Commissioner Dyson Heydon read from Mr Hajje's submission, which said Mr Alex's health was not a matter falling within the royal commission's terms of reference.
It was argued Mr Alex had a right to privacy over his health records and that public airing of his health issues could worsen his health and retard his future income earning capacity.
"Mr Alex has been very clear he actually wants to come down here and clear matters up," Mr Hajje said.
Mr Heydon said he was opposed to the application for confidentiality, but the reasons for this decision were suppressed.
John Agius, the barrister representing the CFMEU, said his client wanted Mr Alex to be called to give evidence.
"We would want to have the issue of the payment of money to an entity, which is recorded on the books as being the CFMEU, properly investigated," Mr Agius said.
Mr Alex's business dealings and associations with high-profile underworld figures have been at the centre of explosive allegations before the commission.
He has been associated with home-grown Islamic State terrorist Khaled Sharrouf and former Comanchero bikie Bilal Fatrouni.
Fairfax Media has previously revealed how Mr Alex cultivated figures in the CFMEU and big building companies who supported his labour hire and scaffolding operations.
Union official Jose Barrios told the royal commission in September he received a threatening phone call from Mr Alex in late August after Mr Barrios questioned CFMEU NSW secretary Brian Parker about why the union was negotiating a workplace agreement with one of Mr Alex's businesses.
The 44-year-old Mr Alex has no criminal convictions apart from a driving offence in 1991, but was charged last month with making death threats to a woman and her family through emails and text messages.
