The Court of Appeal rejected claims the guilty verdict returned against Paul Patterson was rendered unsafe by the jury hearing details about a previous firearms offence.
Patterson, 56, from Drumhoy Drive, is serving a sentence for possessing up to 37 rounds of ammunition in suspicious circumstances.
Police discovered the haul during searches carried out in September 2019.
A box containing the bullets was found in a rucksack along with a Marigold glove containing Patterson’s DNA.
He accepted owning the bag and some of its contents, but denied any connection to the ammunition.
Patterson claimed that he wore gloves when carrying out household chores for his mother, and that the bullets were hidden by someone else unknown to him.
But in 2020 a jury rejected that account and found him guilty of the possession charge.
With Patterson having admitted separate drugs offences, he received a three-year sentence.
His appeal against the guilty verdict centred on the trial judge’s decision to admit bad character evidence.
That related to a conviction at Sheffield Crown Court back in 2004 for possession of an imitation firearm.
Dismissing the challenge, Mr Justice Colton expressed concerns about how the trial judge dealt with the issue in her closing.
But he concluded that she was entitled to allow the evidence.
“The prosecution case was a strong one and the admission of the conviction did not serve to bolster a weak case,” he said.
“The issue of the appellant’s previous conviction was left to the jury in a fair way by the judge and it did not play an inappropriate or disproportionate role in the proceedings.”