Jurors in the Angelika Kluk trial must find the courage to believe that a priest was involved in the Polish student's death, a defence lawyer said.
The Angelika Kluk murder trial is now drawing to a close
QC Donald Findlay said the Crown had failed to prove who had killed Miss Kluk and urged jurors to avoid a "catastrophic miscarriage of justice".
Mr Findlay's client, handyman Peter Tobin, 60, denies raping and murdering Miss Kluk in Glasgow last September.
Jurors are expected to start considering their verdicts on Friday.
During a four and a half hour closing address, Mr Findlay said that there had not been a microscopic fragment of evidence linking his client with the murder weapons - a knife and a table leg.
Prosecutors, Mr Findlay also argued, had failed to demonstrate exactly when Angelika Kluk had been killed or when her body had been hidden.
Earlier the QC had appealed to the 15 jurors to consider all the evidence, not just bits of it as presented, he said, by the advocate depute.
Mr Findlay suggested it had been a strange and bizarre tale involving extraordinary characters less believeable than an episode of the television drama series Taggart.
The judge, Lord Menzies, began his direction to jury members on Thursday and will complete it on Friday morning, after which they will go out to discuss their verdicts.
'Obsession for murder'
Mr Findlay made his closing speech to the jury on the 24th day of the trial at the High Court in Edinburgh.
The lawyer said the prosecution's closing speech, asking the jury to convict Tobin, had been short and concise.
He said: "The Crown chose to pick bits of evidence and present them to you. The Crown are entitled to ignore vast swathes of evidence - as they did."
The lawyer told the eight women and seven men that Tobin had denied murdering Angelika, 23, by his plea of not guilty. After that he had nothing to prove.
Mr Findlay said: "Is it my job to prove to you 'If it wasn't Peter Tobin who was it?' The answer to that is 'Certainly not'.
"I do not intend to make any attempt to prove to you who did kill and murder Angelika."
The lawyer reminded jurors of evidence about St Patrick's priest, Father Gerry Nugent, 63, who told the court he had a sexual relationship with Angelika.
Donald Findlay QC made his closing remarks at the Angelika trial
Mr Findlay said sometimes it was necessary to reach down deeply and find the courage to face the truth.
He said that Father Gerry and alcoholic Matthew Spark-Egan seemed to know a lot about where and how the student's body was hidden, when he claimed they could not have learned it from any external source.
He added: "The fact is there is now clear evidence to entitle you to conclude that a man with an obsession for murder and a parish priest in the city of Glasgow were involved in the death of Angelika Kluk.
"We are asking you to do justice to two people - Angelika Kluk and Peter Tobin. In these courts we do try to do justice, to the dead and to the living.
"It is no justice for Angelika Kluk to convict somebody who should not be convicted."
Mr Findlay said: "You are not here as amateur detectives. You are here to look at the evidence the law has allowed to be presented to you."
On Wednesday, advocate depute Dorothy Bain, prosecuting, told jurors there was a "powerful, compelling and overwhelming case against Peter Tobin".
The Polish student's body was found under the floor of St Patrick's Church in Anderston, Glasgow, last September.
Ms Kluk, 23, had been staying at the chapel house attached to the church and working as a cleaner to help finance her language studies in Gdansk.
The trial continues.