Rolf Harris has had one of 12 indecent assault convictions overturned by the Court of Appeal.
Three judges ruled the conviction was "unsafe".
But Lord Justice Treacy, Mrs Justice McGowan and the Recorder of Preston, Judge Mark Brown rejected his applications to challenge the 11 other indecent assault convictions.
The artist and musician was convicted of 12 indecent assaults at London's Southwark Crown Court in June 2014, one on an eight-year-old autograph hunter, two on girls in their early teens, and a catalogue of abuse against his daughter's friend over 16 years.
Harris was jailed for five years and nine months after being convicted of assaults which took place between 1968 and 1986.
The Australian-born television presenter has since been released from that sentence.
The prosecution did not seek a retrial on the one count and the judges agreed that a further trial would not be in the public interest.
Harris was not in court for the ruling by the appeal judges.
The quashed conviction related to an allegation Harris indecently assaulted an eight-year-old girl in 1969, when she attended an event at a leisure centre in Portsmouth.
But the judges refused Harris permission to appeal against the rest of the 2014 convictions.
They ruled that "stepping back and looking at the totality of the evidence" on those remaining counts "we find nothing that causes us to doubt the safety of those convictions".
Stephen Vullo QC, for Harris, had presented four grounds of appeal at a recent hearing, which Harris attended.
One ground was that there was "fresh" evidence which supported Harris's case, and complaint was also made about a direction given to the jury by the trial judge relating to the credibility of complainants.
In May this year, Harris was formally cleared of unconnected historical sex offences, which he had denied.
He was formally cleared of four counts of indecent assault against girls as young as 13 after a retrial ended with a hung jury.
