Judges have allowed two further grounds for appeal in the case of a man jailed for killing four members of a family.
David Morris is claiming that his 2002 murder trial was unfair
David Morris, 42, is serving four life sentences for the murders of Mandy Power, her young daughters Katie and Emily and her mother, Doris Dawson, 80.
On Wednesday, his lawyer introduced new grounds of "fresh evidence" and "non-disclosure" of surveillance tapes.
Morris is also appealing on the grounds that he did not receive a fair trial and that his convictions were unsafe.
On Thursday, the appeal was adjourned until early April, on a date yet to be fixed.
Morris' legal team, headed by Michael Mansfield QC, said the first new grounds related to the "non-disclosure" of audio tapes made as part of covert surveillance which took place during the murder inquiry.
Mr Mansfield said the other new ground was "fresh evidence" relating to allegations by twin brothers and serving South Wales Police officers, Stephen and Stuart Lewis.
Both men had originally been arrested in relation to the investigation following the June 1999 murders.
Stephen Lewis had been arrested on suspicion of murder while Stuart Lewis had been arrested on suspicion of perverting the course of justice. Both were released without charge.
They had made allegations against police officers, the court heard, some of which were criminal and some disciplinary, but the claims were not fully investigated until after Morris's conviction, when they were found to be unsubstantiated.
Morris claims Mr Hutchison had a conflict of interest at the trial
Stephen Lewis had given evidence as a prosecution witness during Morris' trial.
But Mr Mansfield said that certain officers could have been called to court to dispute what Mr Lewis was claiming.
He said: "Forty officers could have been called to say, in effect, that Stephen Lewis is talking rubbish. That is compelling material."
The claims came after Morris' solicitor at the 2002 murder trial, David Hutchison, gave evidence for a second day, repeating his denial that he had had a conflict of interest in representing Morris.
Mr Hutchison is a criminal lawyer in south Wales who also represented Stephen and Stuart Lewis during their arrests.
Morris' legal team has claimed that Mr Hutchison's professional relationship with the Lewis brothers should have prevented him representing Morris at the murder trial.
Mr Mansfield told the court that David Hutchison had a "serious conflict of interest" which had been a "fundamental flaw" in his decision to act for Morris.
Mandy Power and her daughters were killed at the family home
He said: "Here we have a very experienced solicitor, a solicitor who has been clearly respected by many.
"A person whose reputation, as he said, is on the line. A solicitor who has a desire to have an overview of the case."
But, he added: "The conditions under which this defendant was placed did provide a substantial disadvantage because he was represented by somebody who was compromised.
"Due to an unusual set of circumstances, David Morris has been deprived of his right to a fair trial."
Mr Hutchison, answering earlier questions, again said he 'refuted' the allegation.
He said: "My role was case preparation. I then handed it to leading and junior counsel.
"The decision who was and who wasn't called was made by leading counsel. The way the whole trial was run was decided by leading counsel."