Judge Lord Stewart is expected to ask the eight women and seven men to begin considering their verdict after hearing 50 days of evidence and lawyers' speeches.
The naked body of jeweller's assistant Elaine, 16, was found just yards from her home in Ardgowan Street, Greenock, on the morning of June 2 1986.
She had been strangled, doctors said.
At the High Court in Edinburgh Lord Stewart said there had been no suggestion this was anything but murder - the crucial issue in the case was who did it.
And he warned: "Mistakes about identification have been made in court cases in the past."
John Docherty, 49, now of Dunoon, denies murder and claims that at the time he is alleged to have stripped and strangled Elaine Doyle, 16, he was with his parents - who are no longer alive - at their home in Anne Street.
Docherty has also lodged a so-called special defence of incrimination.
He claims that the culprit might be among a list of 41 names taken from files of the police investigation into the murder.
Lord Stewart is expected to finish speaking to the jury today and to send them to the jury room to begin their discussions.