Leading judges have been urged to overturn sentences imposed on two murderers and a rapist which prevent them ever being released from prison.
Killers David Oakes and Danilo Restivo, and the "Bermondsey Beast" rapist Michael Roberts are all subject to "whole-life" orders - which mean they can never apply for release on parole.
Five judges at the Court of Appeal in London on Wednesday were also asked to reduce the 30-year minimum term imposed on a man who was jailed for life after he "executed" a stranger in the street.
(From the left) Michael Roberts, David Oakes, Danilo Restivo and Kiaran Stapleton
Kiaran Stapleton, 21, who labelled himself "Psycho" when he appeared in court, shot Indian student Anuj Bidve, 23, at point blank range in Salford, Greater Manchester.
Stapleton, Oakes and Roberts all watched today's proceedings - before the Lord Chief Justice, Lord Judge, and four other judges - via video link from their respective prisons.
Oakes announced at the beginning of the hearing that he wishes to "appeal against my conviction".
Rapist Roberts, who terrorised elderly women in a London suburb for more than a decade, was jailed in January and told he will live out his days behind bars.
Roberts, now 46, joined a small group of "life means life" prisoners after raping three victims - one aged 83 - and viciously attacking a fourth in Bermondsey, south London.
Kiaran Stapleton shot Anuj Bidve in the head at point blank range in Manchester
He evaded justice for 15 years but was captured after a cold case review by Scotland Yard.
Hair fetishist Restivo was given a whole life tariff in June 2011 for the "depraved" and "callous" murder and mutilation of a mother-of-two in Bournemouth.
The Italian national, now 40, was found guilty by a jury at Winchester Crown Court of the 2002 murder of neighbour Heather Barnett, 48.
Oakes, now 51, of Canney Road, Steeple, Essex, who "sadistically tortured" his former partner before shooting her and their two-year-old daughter, was told at Chelmsford Crown Court in May that he will never be released from prison after a jury found him guilty.
He went to Christine Chambers's house in Braintree where he killed her and daughter Shania with a shotgun.
Lawyers for those currently subject to a whole-life order are asking the court to set a minimum term instead.
David Perry QC, for the Crown, said it was seeking to "support the whole-life orders made in the cases of Oakes and Restivo", and the minimum term imposed in Stapleton's case.
In the case of Roberts it was conceded that the making of a whole-life order was "wrong in principle".
But he stressed that in making such a concession, "we are not seeking to minimise the seriousness of the offences".
He added: "Our submissions are intended to reflect the fact that a whole-life order is reserved for rare cases of exceptional gravity, where a whole-life order is made for the purpose of pure punishment, and not for public protection."
During the proceedings one of the judges, Lord Justice Leveson, emphasised that the issue being considered by the court was not about "letting people go".
Offenders become eligible to apply for parole once their minimum term has expired, but they are not released until they are deemed to no longer represent a risk to the public.
Lord Justice Leveson said that if an offender was not safe to release, then they should stay in prison for "as long as it takes and if that is forever then so be it."