Former soldier John Docherty strangled Elaine Doyle yards from her Greenock home as she returned from a disco in 1986.
He lived a seemingly normal life until police re-examining the case knocked on his door two years ago. DNA recovered from the 16-year-old's body was linked to Docherty.
A police source said officers would leave "no stone unturned" in the search for other potential victims. It is understood they will investigate any new information about Docherty's past.
A Police Scotland spokeswoman said: "All unresolved murders are continually reviewed and if any new information comes to light it will be investigated."
Docherty still lived in Greenock, less than a mile from the lane where the murder happened.
It is believed police "haven't ruled out the possibility" the father-of-one could have been involved in other crimes. About 70 murders, going back more than 100 years, remain unsolved across Scotland.
The Elaine Doyle murder was the first case to go to trial following an investigation by the new Crown Office cold case unit.
It was launched in 2011, with Scotland's top law officer, Lord Advocate Frank Mulholland, QC, vowing to snare killers who had evaded justice.
Docherty, 49, agreed to a mouth swab DNA test after officers working on the inquiry visited his home.
A 50-day trial heard how the chances of the DNA belonging to anyone else were about a billion to one.
Ms Doyle's mother Maureen said: "The result at court doesn't make our day-to-day living any easier. The pain doesn't go away. But my son John and I take comfort that we now have justice for Elaine, which is all we, especially her dad Jack, campaigned for."