The case has been one of Australia's highest-profile mysteries for more than two decades, and came to be known as the Claremont serial killings.
Bradley Robert Edwards, 51, denied killing Jane Rimmer, 23, Ciara Glennon, 27, and Sarah Spiers, 18, in Perth.
On Thursday, a judge convicted him of Ms Rimmer and Ms Glennon's deaths.
But Justice Stephen Hall said there was not enough evidence to convict him of murdering Ms Spiers.
