Steven Barker received a life sentence for the rape
One of three people jailed over the killing of Baby Peter is seeking permission to challenge his conviction for raping a two-year-old.
Steven Barker, 33, was the boyfriend of Tracey Connelly - the mother of Peter who died in north London in 2007.
Barker was jailed for 12 years for causing the death and must serve a minimum of 10 years for raping a girl.
Barker's case is being heard at the Court of Appeal by Lord Chief Justice, Lord Judge, and two other judges.
He was not in court for the hearing.
The rape victim was four when she became the youngest ever person to give evidence to the Old Bailey.
Jurors in the case also saw a police video, made when she was three, in which she used a doll and a teddy bear to show how Barker had attacked her.
BBC correspondent John Andrew said Barker's lawyer Bernard Richmond QC told the hearing that the child was too young to be a competent witness at his trial.
At issue, Mr Richmond said, was the ability of the girl to properly answer questions put to her and the delay in bringing the case to trial.
He said that when the girl gave evidence at the Old Bailey at the age of four she was being asked to recall events that, to her, "were a lifetime ago".
He said many of her answers were "mere nods or shakes of the head" and there were also frequent silences.
But Sally O'Neill QC, for the Crown, argued that the girl had been able to answer questions properly and that she had been able to give a clear description of what had happened.
She said it had not been possible to avoid the delay before the case reached trial and that the wait had not affected the girl's memory of the attack.
The girl was a competent witness and the nodding and shaking of the head only happened because she was tired, Miss O'Neill said.
Suggestions of recording a cross examination were put forward by the judge, she added.
Barker was jailed over the death of Peter at the Old Bailey in May, along with Tracey Connelly, 28, and lodger Jason Owen, 37.
At the time the judge told Barker he played a major role in the death of Peter, who was found in a blood-stained cot with more than 50 injuries.
Connelly recently dropped an appeal against her indefinite sentence with a minimum five-year term.
But Owen did win a challenge against his indefinite sentence, which was changed to an indeterminate sentence with a three-year minimum.