A businessman fighting for the "right to be forgotten" over a past crime has won a High Court action against Google.
The ruling in the man's favour was made by a judge in London on Friday.
But Mr Justice Warby rejected a similar claim brought by a second businessman who was jailed for a more serious offence.
The judge announced his decisions in the two cases, which were both contested by Google, following separate High Court trials.
Both businessmen, who were convicted of criminal offences many years ago, argued that their convictions were now legally "spent", and that they have been rehabilitated.
Lawyers said their claims, which were brought under data protection law and for "misuse of private information", were the first of their kind to be aired in England.
Mr Justice Warby said the businessmen, who cannot be named for legal reasons, complained of results returned by Google Search that feature links to third-party reports about their convictions.
Their claims were based, he said, on the "right to be forgotten", or "more accurately" the right to have personal information "delisted" or "de-indexed" by the operators of internet search engines.
The businessman who lost his case to be "delisted" complained about three links returned by Google providing information about his conviction for "conspiracy to account falsely", for which he received a sentence of four years.
The businessman who won was sentenced to six months' imprisonment for "conspiracy to carry out surveillance" and in his case, which related to complaints about 11 "source publications", the judge said an "appropriate delisting order should be made".
However, the judge ruled out any damages payment.