Police have stopped the investigation into murdered student Jessie Earl following discussions with her parents.
The police team charged with finding the Eastbourne woman's killer has now been disbanded, although the case will remain open.
The skeletal remains of 22-year-old Jessie were found in bushes on the Downs at Beachy Head in 1989.
She had been missing from her home in Upperton Gardens, Eastbourne, since 1980.
The murder investigation was re-opened in January and included an appeal on BBC TV's Crimewatch programme, following which a number of people were interviewed and the site where Jessie's body was found revisited.
Detective Chief Inspector Steve Dennis, who headed the operation to solve the 11-year-old murder, said the effort had failed to shed light on the death.
He said: "At the moment the case remains open but we have seen Jessie's parents and they have agreed we cease to continue.
"They understand perfectly and have worked very closely with us.
"We have made some headway but we have found nothing substantial towards solving the inquiry."
Attempts to find clues that may lead to Jessie's killer have included a forensic search of the Downs and an operation using members of a local metal detecting club.
The search unearthed rusting pieces of jewellery but none was recognised by Jessie's parents, John and Valerie.
Anyone with information relating to Jessie's death is asked to contact Mr Dennis on 0845 60 70 999.
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