Three judges in the Court of Appeal reserved their decision yesterday after hearing legal argument in a plea by Sutcliffe for his "whole life" tariff to be overturned.
His counsel, Edward Fitzgerald QC, argued that his "mental disorder" justified the imposition of a minimum term - the least a prisoner must serve before becoming eligible to apply for parole - of a "finite" number of years instead.
Mr Fitzgerald said: "We accept that the applicant was convicted of the brutal murder of 13 women and the attempted murder of seven others and, on the face of it, we accept that the number and the nature of the murders is such that would call for a whole life tariff.
"The sole submission in this case is that the disorder suffered, and still suffered by the applicant, is a sufficient mitigating circumstance to justify a long, finite term of years instead of a whole life tariff."
The former lorry driver, from Bradford, West Yorkshire, was convicted at the Old Bailey in 1981.
Sutcliffe, now 64, received 20 life terms for the murder of 13 women and the attempted murder of others in Yorkshire and Greater Manchester.
He is being held in Broadmoor top-security psychiatric hospital after being transferred from prison in 1984 suffering from paranoid schizophrenia.
Peter Wright QC, opposing the appeal on behalf of the Crown, submitted that there was "no mitigation capable of displacing the starting point of whole life" for what he described as a "terrible catalogue of crimes".
Mr Fitzgerald invited the judges to find that there was "at least a reasonable possibility that he suffered from mental disorder and that it did diminish his responsibility".
Reserving judgment, the Lord Chief Justice, Lord Judge, sitting in London with Mr Justice Calvert-Smith and Mr Justice Griffith Williams, said there was "a great deal of material for us to work our way through" and the court would give its decision in writing "in due course". No date was given for the announcement.
It was on 5 July 1975, just 11 months after his marriage, that he took a hammer and carried out his first attack on a woman.
Sutcliffe, now known as "Peter Coonan", is challenging a "whole life tariff" ruling by Mr Justice Mitting on 16 July.
Mr Justice Mitting, when setting a whole life tariff, said the primary submission made on behalf of Sutcliffe was that the degree of his responsibility "was lowered by mental disorder or mental disability".But the judge said: "These propositions were, however, unquestionably rejected by the jury."
He ruled: "It is not, in my opinion, open to a judge, setting a minimum term, to go behind the verdict of the jury by concluding that, although the defendant's responsibility was not proved to have been substantially diminished, he should be given the benefit of the doubt for the purpose of setting the minimum term, by concluding that it might have been."