The first person in the world to be convicted of murder on the basis of DNA evidence is challenging his sentence.
Colin Pitchfork, now 48, who was jailed for life 20 years ago for the "heinous" murders of two schoolgirls in Leicestershire, is currently serving a minimum term of 30 years.
But Pitchfork claims the 30 years is "manifestly" excessive and wants it reduced to 20 years - meaning he would be eligible to apply for release on parole.
He was granted permission to appeal by judges in the Court of Appeal in London in December.
They ruled that his case raised "arguable" issues, but warned that they did not think the sentence would be cut when his case was heard fully by the court.
Lord Justice Stanley Burnton, sitting with two other judges, said at the time: "We do not hold out great hope to the appellant that in the end the period of 30 years, which is a substantial reduction from a whole life tariff, will be reduced by this court..."
The offences committed by Pitchfork, he said, were of the "most serious and terrible kind".
Pitchfork, a baker, was jailed at Leicester Crown Court in 1988 after pleading guilty to two offences of murder, two of rape, two offences of indecent assault and one offence of conspiracy to pervert the course of justice.
His first victim was 15-year-old Lynda Mann, of Narborough, who was murdered in 1983. Dawn Ashworth, also 15, from Enderby, was killed in 1986. Both girls were raped and strangled.
Pitchfork is challenging the setting of his tariff at 30 years last August following a review by a High Court judge.
