It was the lack of evidence over what happened after the teenagers left the World's End pub which proved fatal to the Crown case against Angus Sinclair.
The girls had been on a night out at the World's End pub
Defence QC Edgar Prais successfully argued there was nothing to show the girls had been abducted from Edinburgh.
There was no evidence to show any sex encounter between Sinclair and the girls had not been consensual.
Although it was beyond question they were murdered, there was no evidence to link Sinclair to their deaths.
Two man job
Mr Prais told judge Lord Clarke: "If there had been DNA on a ligature, something of that nature, I don't think I could stand here."
The Crown had insisted that Sinclair and his brother-in-law, Gordon Hamilton, were in it together.
Mr Prais told the court: "What we have got here is two girls, bound and strangled and battered.
"There is no evidence that because there are two deceased this is something only two people could do together.
"There is no evidence this had to be a two man job."
The lawyer said: "The evidence is consistent with it being perpetrated by one person and - if it is one person - there is no way a jury can be asked to adjudicate."
He told the court: "Let's say there was evidence of DNA on a ligature. If there was DNA from two accused, or Sinclair, that would be a different cup of tea but there is absolutely nothing."
Mr Prais concluded: "There were no eye-witnesses. The Crown have got to build this case on science. That is very difficult."
The lawyer's arguments, which cleared Sinclair, were made after the jury had been sent home and could not be reported before Lord Clarke had delivered his ruling on Monday.
The judge told the lawyers: "I have reached the conclusion that the submissions made by the senior counsel for the accused are sound and have not been adequately rebutted by the Crown."
The judge said: "I am of the view that the evidence, taken at its highest in the context of both the evidence as a whole and evidence that does not exist is neutral."
The decision could not be left to the jury, he said.
"As far as the murders themselves were concerned there is no forensic evidence linking the accused to items used to kill the girls."
Lord Clarke added: "It goes without saying, we are not in the realm of suspicion.
"The question for the court is rather whether there is sufficient in law for the jury to infer safely and beyond reasonable doubt that the accused was involved in any or all of the crimes libelled."