Google has been generally reluctant to honor European Union "right to be forgotten" requests when people try to hide their past convictions, but it a new ruling, the company may have a hard time not honoring some future requests.
The man who lost his case was convicted more than 10 years ago of conspiring to account falsely.
Mr Justice Warby said the businessmen, who can not be named for legal reasons, complained about Google Search results which featured links to third-party reports about their convictions.
The judge ruled out any damages payment, and told the court: NT2 has frankly acknowledged his guilt and expressed genuine remorse.
NT1 was given permission to appeal after losing his case.
"Spent convictions are rather different".
The judge said the information related to his crime retains sufficient relevance today. In those circumstances, "the public interest in having information with his name about this case doesn't prevail".
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'He remains in business, and the information serves the goal of minimising the risk that he will continue to mislead, as he has in the past, ' he said.
'We are pleased that the Court recognised our efforts in this area, and we will respect the judgements they have made in this case'.
The Right to Be Forgotten can be interpreted in various ways by courts throughout Europe. He claimed that the information was no longer relevant and that it should be deleted.
In May 2014, the European Court of Justice (ECJ) said links to irrelevant and outdated data should be erased from searches on request.
In a ruling last month, Paris judges said that Google had to reduce the visibility of stories about a former chief financial officer at a French company who was fined 200,000 euros ($247,000) for civil insider-trading violations.
"The Court will have to balance the public's right to access the historical record, the precise impacts on the person, and the public interest".
"The search result in question involved a decade-old criminal conviction, reportedly for 'conspiracy to intercept communications.' A similar case was decided the other way by the court".