Restrictions that prevent the reporting of the detail of a semi-secret terror trial should be lifted, lawyers for the media have said.
The defendant in the trial, Erol Incedal, was cleared on Thursday of planning a terrorist attack.
Journalists from organisations including the BBC heard some of the secret evidence, but they have not yet been allowed to report it.
Mr Justice Nicol said he would reveal his decision next Wednesday.
Turkish-born Incedal, 27, from London, was found not guilty after the jury had deliberated for 27 hours.
But most of his trial was held in secret and the details of the accusation against him can still not be reported.
Secrecy ‘not justified’
The barrister for the media, Anthony Hudson QC, told the Old Bailey in London that the restrictions should be lifted so that the public could understand the nature of Incedal’s defence and gain some insight as to why he was acquitted.
He argued that secrecy was no longer justified on the grounds of national security.
Prosecutors are opposed to the lifting of reporting restrictions.
Incedal’s lawyers did not make any submissions in open court.
During the public sessions of Incedal’s trial, the jury heard the married father-of-two had travelled to Syria, where he met a fighter known as Ahmed.
The pair discussed, via email, doing terrorist attacks in the summer of 2013, jurors were told.
Prosecutor Richard Whittam QC said the men were talking about the murder of an individual of significance or an attack such as that in Mumbai, where automatic rifles were used and a number of people killed.
The prosecution said Incedal’s plans were scuppered by police who bugged his car after he was stopped for speeding in September 2013.
The listening device recorded him talking about buying a gun and his time in war-torn Syria.
Incedal denied that he had been planning a terror attack.
The law student will be sentenced on Wednesday for possessing a bomb-making guide, having been convicted of that offence last year.