Google bosses have mounted a "public interest" defence after two businessmen took historic High Court action in a bid to stop their names being linked to internet media reports about past crimes.
The two men say convictions are more than a decade old and legally "spent".
Both argue that they have a "right to be forgotten" and want Google to stop linking their names to articles on news websites.
A judge has begun to consider evidence relating to the first man.
Mr Justice Warby, who says the men cannot be named in media reports of the litigation, heard that the first man had been convicted of "conspiracy to account falsely" in the late 1990s.
He is overseeing a trial at the High Court in London which is expected to last several days.
The second man's case is due to be analysed at a further trial in the near future.
Lawyers representing Google say the cases are to first "right to be forgotten claims" aired in an English court.
Barrister Antony White QC, who is leading Google's legal team, told Mr Justice Warby that Google had "declined to delist".
"The claimants are businessmen who have current business interests which may involve interaction with actual and potential customers and investors and others, and who have posted statements online about their business experience and expertise," he said.
"The material in question is materially accurate."
He added: "There are strong public interest reasons for maintaining access to the publications."
Barrister Hugh Tomlinson QC, who is representing the first businessman, said the information at the centre of the case was "spent" under legislation relating to the rehabilitation of offenders and had become "private".
"There is a strong public policy in favour of the rehabilitation of criminal offenders," he said.
"The claimant has served his sentence and the rehabilitation period has expired."
Mr Tomlinson said the man had not been charged with any subsequent offence.
He added: "Google should not, by the application of its own standards of morality, undermine the clear policy of Parliament."