Last week, the inquiry into the conviction of Eastman for the 1989 killing of Assistant Federal Police Commissioner Colin Winchester heard evidence from John Dee, a former deputy head of the Commonwealth Director of Public Prosecutions and Victorian County Court judge.

Mr Dee was at the inquiry to give evidence of the warnings he gave to police six years before the trial about the reliability of a key forensic witness, Robert Barnes, whose analysis of gunshot residue would help link Eastman to the murder scene.

That evidence ties in with one of the aims of the current inquiry: to establish whether there was proper disclosure to Eastman's defence of information casting doubt on the veracity and reliability of Mr Barnes.

But Mr Dee's evidence to the inquiry went further: he was a counsel assisting during part of the inquest on Winchester.

Mr Dee said he and his colleagues never believed there was enough evidence to convict Eastman.

''We never, ever considered there was enough evidence to convict Eastman of murder beyond reasonable doubt,'' he said.

''He should never have been convicted on the evidence.''

Acting Justice Brian Martin said the former prosecutor's opinion was not particularly relevant to the inquiry but the fact he disclosed his concerns about Mr Barnes to the Australian Federal Police might be.

Mr Dee left Canberra and the inquest in May 1990, before the inquiry was ultimately completed.

He had no involvement in the trial and said he had only read the transcript of the Crown's opening submission against Eastman and was not aware of all the witnesses who gave evidence.

Mr Dee said he was ''appalled'' over the use of Mr Barnes, whom he had observed during the Russell Street bombing trial over the 1986 attack on Victorian police headquarters.

The prosecutor formed an ''adverse opinion'' of Mr Barnes at the time, after overhearing remarks made to police in casual conversation in 1988 at a celebration after the return of verdicts in the high-profile case.

Two men were found guilty of the bombing and another two were acquitted.

''The remark he made was that we should have convicted the two who were acquitted,'' Mr Dee told the inquiry last week.

He told the inquiry the use of the word ''we'' stuck in his mind.

The former prosecutor said he was concerned about the way Mr Barnes had given evidence during the Russell Street bombing trial.

He said that he did not think he had been acting as an independent witness and was trying to be the ''star of the show''.

Mr Dee later moved to the ACT and learnt while assisting the inquiry into Mr Winchester's death that Mr Barnes was doing some of the forensic work on the case.

''I was very concerned. In fact, I was appalled that he should be brought in,'' he said.

He contacted the Australian Federal Police, both verbally and in writing, advising them to use an expert in Britain to double-check Mr Barnes' work.

Mr Dee said he received ''not a word'' in response to his memo. The work of Mr Barnes was, however, extensively peer-reviewed, including by overseas experts.

Under cross-examination by Mr Barnes' counsel, Ian Freckelton, SC, Mr Dee said he had not known that Mr Barnes received a police commendation for the quality of his work on the Russell Street bombings, nor that he was a chartered expert in engineering and explosives.

He also said he had not known that others in the United States, Britain and Israel reviewed and analysed Mr Barnes' work, as he had suggested to the AFP.

James Robertson, a professorial fellow at the University of Canberra and the director of the National Centre for Forensic Studies, also gave evidence to the Eastman inquiry last week. Professor Robertson was formerly the head of AFP forensic services from about 1989 to 2010.

Soon after taking up his role with the AFP, he said he expressed concerns about Mr Barnes and whether he was qualified to undertake the forensic work involved in the Eastman case.

Professor Robertson said in an affidavit he had believed Mr Barnes oversold his qualifications and went too far in the witness box.

He said that he had told the head of the investigation, Commander Richard Ninness, of his concerns.

He said he told him that Mr Barnes' work should have been reviewed.

The inquiry is expected to resume on Wednesday.