Three men who plotted the biggest gem heist in UK history have begun an appeal, claiming the judge fell asleep during their trial.
The Millennium Star was among the De Beers collection
Four men were convicted of conspiracy to rob after trying to steal £200m of diamonds from London's Millennium Dome.
Lawyers say that Judge Michael Coombe may have missed vital evidence and say their clients' sentences and convictions should be reduced.
Judge Coombe admits falling asleep but denies snoring loudly, the court heard.
It is just one of the grounds of appeal to be considered during the two-day hearing at the Court of Appeal.
Raymond Betson, 41, from Chatham in Kent, and William Cockran, 50, from Catford, south-east London, are serving 18-year sentences.
They claim they should have faced a lesser charge of conspiracy to steal.
Aldo Ciarrocchi, 33, of Bermondsey, south-east London, wants his 15-year sentence reduced, but is not challenging his conviction.
The men were part of a group who used a mechanical digger to smash their way into the Dome which housed the De Beers diamond exhibit vault in November 2000.
But more than 100 armed police, acting on a tip off, were lying in wait and caught them.
They were convicted at the Old Bailey in February 2002 and sentenced by the then 70-year-old Judge Coombe.
Lawyers for Betson and Cockran will call two witnesses, a freelance journalist working for the BBC's Panorama programme and a court clerk, to say the judge fell asleep.
Defence counsel Edmund Romilly told the court anyone could have momentary lapses of concentration.
"But it is another matter if there is sleepfulness accompanied by noises associated with sleep, drawing attention to the person who is asleep and deflecting the jury's attention," he said.
"It would raise in the minds of the jury the impression that the judge had such a dim view of the defence case that he could not be bothered to stay awake."
But Lord Justice Rose told the court: "The judge very frankly admits he was asleep. It doesn't matter whether he was snoring or not. If he was dozing off, he wasn't paying the attention he ought to have been.
"It is perfectly plain that judges should not fall asleep. The question we have to address is whether it is arguable that, in consequence, these convictions were unsafe."
The Court of Appeal has already dismissed an appeal by a fifth man, Kevin Meredith, who is serving five years for conspiracy to steal.