The State's case against two former Anglo Irish Bank officials, jailed for conspiring to conceal or alter bank accounts being sought by the Revenue Commissioners, was astonishingly weak, the Court of Appeal has been told.

Tiarnan O'Mahoney, 56, of Glen Pines, Enniskerry, Co Wicklow and Bernard Daly, 67, of Collins Avenue, Whitehall, Dublin had denied knowingly furnishing false information and conspiring to defraud the Revenue, as well as conspiring to have accounts deleted from the bank's internal system.

Having been found guilty by a jury at Dublin Circuit Criminal Court, Judge Patrick McCartan jailed O'Mahoney for three years and Daly for two years on 31 July 2015.

Last December, the Court of Appeal quashed an 18-month sentence imposed on the two men's co-accused, Aoife Maguire, a former Anglo assistant manager, for her role in the conspiracy.

The court found the sentence was too severe and substituted a new nine-month sentence in its place, suspending any unserved portion, releasing her from prison.

Yesterday, O'Mahoney, who had been second in command at the bank and Daly, the banks former company secretary, opened appeals against their convictions.

Counsel for Daly, Seán Guerin SC, told the Court of Appeal the case against his client on the furnishing of false information was "fundamentally weak" and "non-existant" on the other two conspiracy counts.

In their appeal papers, Mr Guerin said the prosecution did not now actually say why Daly was guilty of anything and why the jury was right.

He said the prosecution had mislead the jury on what the case would be at the outset, on what the case was at the end and he did not know how a trial court could conclude that the State's presentation of the case was fair or accurate.

They were "filling in the (evidential) gap", he said, by misleading the jury on "incredibly important factual matters".

He further submitted that on the morning of the trial, the prosecution extended the dates on the indictment so that the single act alleged against Daly could also be used in aid of the conspiracy charges.

It was the "root of all evil" which occurred to his client, Mr Guerin said.

The prosecution was anxious to describe a long standing conspiracy. If there was one, Mr Guerin said, it was hatched in March 2003, months before Daly had any involvement in it.

Mr Guerin said there had been no real investigation into the production of the list, from which certain information was omitted.

Nobody had ever asked where the list had come from, who produced it or who gave it to Daly, Mr Guerin said.

"That's how weak the case was". It was an "astonishing weakness", Mr Guerin said.

The list could have been created in a number of ways, he said. It was possible someone used a previous list from 2003 as a starting point.

It was possible the IT people who might have produced the list did not programme their computers properly.

Mr Guerin said the person who conducted the investigation upon which the prosecution relied, a fraud investigator within Anglo, Patrick Peake, had "a conflict of interest".

Mr Peake was a member of the task team and the reality was that the garda investigation was Mr Peake's investigation, Mr Guerin said.

Counsel further submitted that there were substantial errors and omissions in the judge's charge to the jury.

The trial judge had confused two lists made in June and November 2003, had incorrectly told the jury that it was known the list was created by the task team and incorrectly told them that a chief prosecution witness was directed not to include a particular account

While the judge said Daly was anxious to exclude people from the task team, he was actually anxious to include them, Mr Guerin said.

Those errors were fatal to any notion of Daly receiving a fair trial, counsel said.

Mr Guerin will continue making submissions before Mr Justice George Birmingham, Mr Justice Garrett Sheehan and Mr Justice John Edwards tomorrow.

Gardaí told O'Mahoney was a bully

Earlier, counsel for O'Mahoney, Brendan Grehan SC, concluded his submissions on a ground of appeal in relation to the admission into evidence of Daly's unedited garda interview.

Daly had told gardaí in the interview that O'Mahoney was a bully, of whom a chief prosecution witness,  the bank's former Head of Compliance Brian Gillespie, was terrified.

There was not any cogent reason put forward at all as to why this evidence was necessary or admissible, Mr Grehan said.

From the safety of an interview Daly could never be cross-examined on, he was claiming that the man sitting beside him in the dock was a bully who terrified staff, counsel said.

It was damning for one accused to point the finger at another accused.

It damned O'Mahoney in front of the jury in a manner in which he could not respond and there was simply no way of dealing with it, Mr Grehan said.

An application was made to the trial judge on the basis that in a separate trial this material wouldn't have appeared at all.

All matters together meant the possibility of O'Mahoney receiving a fair trial had long gone, Mr Grehan said, and a direction by the trial judge was not sufficiently clear to enable this.

Mr Grehan asked the court to overturn his client's conviction.

O'Mahoney's appeal against sentence was deferred until the outcome of his conviction appeal.