A police notebook in Mr Snow's breast pocket saved him from more serious chest injuries, but he passed out and nearly bled to death from the other wounds.
Rajgopaul also fired at friend, Gavin Lomas, but the shot missed.
He was found guilty in March of one charge of attempted murder, one charge of firing a weapon with intent to cause grievous bodily harm, three charges of unlawfully possessing a firearm, one charge of possessing methamphetamine for supply and one charge of receiving stolen property.
Rajgopaul was sentenced to 14 years in prison for attempting to murder Mr Snow, and a cumulative four years for firing a weapon at Mr Lomas with intent to cause grievous bodily harm.
His nine year total sentence on the other charges was to be served concurrently.
Appeal lawyer Ron Mansfield argued the trial judged erred in his summary to the jury of an expert witnesses' evidence, and evidence over gunshot residue on Rajgopaul's hands.
The Court of Appeal ruled the judge presented the evidence in a fair and balanced manner and dismissed the appeal against conviction.
Mr Mansfield also argued the sentence was too high, but the court found it was appropriate.
However, the Crown identified an issue with the minimum 10-year term handed down, because it had not been applied to a particular charge.
The court therefore quashed the sentence and ordered a new minimum period of 8 years for attempted murder, to be served cumulatively with a two-year minimum for firing a weapon with intent to cause grievous bodily harm.
That means Rajgopaul will still be ineligible for parole for 10 years, as with his original sentence.