Their lawyers had sought home detention - the punishment handed down to the other two directors - citing a disparity in penalties.
Donald Young, 68, who was tried alongside Moses and Doolan, was sentenced to nine months home detention, 300 hours' community work and $310,000 reparation.
The fourth director, John Hotchin - younger brother of Hanover co-founder Mark Hotchin - had earlier entered a guilty plea and testified against his former colleagues.
He received 11 months on home detention, 200 hours community service and was ordered to pay reparation of $200,000.
The offending involved publishing untrue statements in the company's prospectus and in letters to investors between 2006 and 2007.
According to the Crown, the prospectus and other mail-outs failed to disclose the true financial position of Nathans Finance and its significant lending to parent company Vending Technologies Ltd (VTL).
Nathans was placed into receivership by its trustee, Perpetual Trust, in August 2007, owing some $174 million to about 7000 investors.
At the heart of Moses' appeal against his jail term was that he was honest in his dealings as a director, Paul Davison QC told the Appeal Court.
"Any failing he was responsible for was not the result of dishonestly in any way.''
The lawyer disputed sentencing judge Justice Paul Heath's description of "gross negligence.''
Any risks were very well understood.
"They (the directors) were effectively looking at the detail and not the big picture,'' said Mr Davison.
"Yes, they got it wrong - how they got it wrong! It wasn't a case of not trying to get it right.''
But Justice O'Regan said today that ``gross negligence'' was hard to contest.
The public thought they were investing in a finance company, he said. In fact their money was being "gambled'' on loans to VTL.
For Doolan, Chris Tennet said: "Doing what he was doing and falling short (as a director) is a big difference from being dishonest or reckless.''
Mr Tennet denied that his client had shown no remorse.
Both appellants had already served a period of their prison sentences as "older white men'' with all the difficulties that came with that, he said, arguing that they - like their two fellow former directors - should have got home detention.
Justice O'Regan said if the appeals were granted and that was the right sentence, Moses and Doolan would get a home detention adjustment that would take into account how long they had served behind bars.
Representing the Crown, Brian Dickey submitted that the prison sentences were deserved and were "at the light end.''
The offences were committed in the boardroom and should attract sufficient deterrent.
He said offenders "in this area'' tended very much to be people of good character, which was why they were on boards and why investors handed over money "in faith.''
Addressing the sentence disparity, Mr Dickey said the trial judge commented that Young was the least culpable and the only one who appeared to show any real empathy or remorse for the victims.
Young was also the least involved in the business, which he had joined much later than the other directors.
By pleading guilty to three charges - two counts fewer than the others faced - Hotchin was sentenced on what information was before the judge, not what evolved at trial, said Mr Dickey.
That made him eligible for a discount in sentence.
