Curran pleaded guilty to five charges of indecently assaulting two boys between 1989 and 1994 and was jailed for four years last February.
He ranks as one of Northern Ireland's most notorious clerical paedophiles with a catalogue of abuse that includes attacks on 13 boys over a 17 year period.
The pattern in which he abused those children was always the same. Curran was a Priest at St Paul's in West Belfast in the late 80s. He built a friendship with the parents of altar boys and then took them to his isolated cottage near Tyrella Beach in County Down where he plied them with alcohol and sexually abused them.
The sentence he is serving currently is his third custodial sentence. He was first jailed for seven years in 1995 for abusing nine boys; the youngest was only eight years old.
He appealed his sentence last June and appeared via video link as the Lord Chief Justice delivered his judgement on Friday.
"By way of mitigation it was accepted that the appellant's plea was volunteered at the first available and reasonable opportunity," he said.
When arrested in 2011, Curran told detectives he had been a former alcoholic and at that time in his life, had been totally out of control.
The Court of Appeal was told Curran had given up alcohol and that there had been no concern about his behaviour towards children since his release from prison in 1998.
The Lord Chief Justice said, "It appears on each occasion the appellant has entered pleas of guilty at a stage which has prevented any concern that victims would have to give evidence and each judge has considered it appropriate to allow him full credit for those pleas.
"We have also dealt with the issue of remorse."
Concluding, he said he considered that the sentences imposed were "manifestly excessive". As a result Curran's current jail term was reduced from four years to three years.