Justice Secretary Chris Grayling and media organisations are asking judges to overturn an order granting anonymity to a killer who committed "exceptionally horrific crimes".
Barrister Guy Vassell-Adams argued at London's High Court that the order - made in response to fears that the killer's own life was in danger - was legally flawed and wrongly prevented the public from knowing the full facts of the case.
"The full facts are exceptionally horrific by even the standard of murders," said Vassall-Adams.
Chris Grayling, the Justice Secretary, is challenging the anonymity order
He said the order restricted the media to saying they were "three sadistic murders - but that doesn't even give you the half of it".
Even "the nature of the victims" could not be publicised.
The order was made after a legal challenge by the man, referred to as M, who has spent decades in prison, against a Parole Board decision refusing him a transfer to open conditions.
Mr Justice Simon granted anonymity in January when he dismissed M's parole challenge.
He rejected submissions from the Press Association that allowing anonymity set a precedent for other high-profile prisoners to seek similar orders.
Granting anonymity, the judge said in January: "It is no part of the case advanced on behalf of the claimant to minimise what were, on any view, exceptionally horrific crimes.
"Not only did he carry out sadistic, unprovoked and vicious murders, he inflicted further injuries to the bodies of his victims."
Because of the important legal issues raised by the order, Lord Justice Pitcher joined him to create a two-judge court to hear today's media application.
Vassall-Adams told the judges M's lawyers were arguing the case was about "whether the media should be allowed to imperil (M's) life or scupper his chances of rehabilitation".
He said those arguments really applied to a different type of case in which individuals - like Jon Venables and Robert Thompson, who killed James Bulger - were provided with a new identity and there were injunctions against the media aimed at protecting them from being attacked while living in the community.
"The injunction protects confidential information, which is the new identities. It doesn't prevent the media reporting what is already public," said Vassall-Adams.
M had already been in prison over 30 years serving multiple life sentences, since pleading guilty in 1973, and there was no imminent prospect of him being released - "furthermore his identity has not only been public but received massive previous publicity".
Anyone interested in finding out about his crimes could do so by a click of a button on the Internet, said Vassall-Adams.
Not allowing the nature of his victims to be identified "masked" what the case was about, which was the Parole Board's refusal to recommend that he was fit for open conditions.
"Understanding the nature of the victims and the terrible treatment meted out to them gives a completely different complexion to this whole case", said Vassall-Adams.