Jolanta Bledaite's killers must have thought they had committed "the perfect murder", according to the detective who led the murder inquiry.
Detective Chief Inspector Graham McMillan said the fact that Ms Bledaite had made it known she was leaving the country imminently gave her killers the ideal opportunity.
If they were able to erase all trace of her, Aleksandras Skirda and Vitas Plytnykas could create the impression that Ms Bledaite had simply left without announcing the fact.
They would then be free to withdraw money from her bank account without arousing suspicion.
And if her remains had not washed up on an Arbroath beach, said Mr McMillan, there was a "good chance" her murder would have gone undetected.
He said: "I think at the very least it could have been some weeks or even months before next of kin began becoming concerned for Jolanta, that they hadn't heard from her.
"We would have been a long time behind the game if she had been reported missing, and we would then have been looking at a missing person inquiry rather than a murder inquiry in that first instance."
The investigator - who was only into his second day as a Detective Chief Inspector on April 1 2008 - admitted he was "sceptical" when first told about the finding, fearing he was the victim of an April Fool's joke.
But after receiving confirmation of the find, he realised the force was potentially facing a "very long-running investigation".
Key to the inquiry was establishing who the victim was, and help came in the form of Ms Bledaite's employer, who approached the police when Ms Bledaite uncharacteristically failed to appear for work.
An officer in the force also recognised the picture of Ms Bledaite from a separate case when the Lithuanian had helped police by acting as an interpreter.
Having achieved their "major break in the inquiry" by identifying her, officers were led to Ms Bledaite's Brechin flat, and ultimately to Skirda and Plytnykas.
Meanwhile, Interpol assisted by making inquiries across Europe into the suspects, as well as tracing Ms Bledaite's next of kin.
With witnesses in the case ranging so widely in nationality, interpreters were heavily relied upon, some travelling from outside Scotland to assist.
Mr McMillan said the investigation had become "particularly fast-moving once we got the breaks".
The "flaw" in the killers' plan, he said, was a failure to recognise that the place where they chose to dispose of the body parts was always likely to cause them to wash up nearby.
"I think, having disposed of the body in this way and having walked away, my personal view is that they probably felt they had committed the perfect murder," he said.
"You have a young woman who made it quite clear to those who knew her that she was intending leaving the country shortly. They left no trace of her behind as far as they could see and had previously disposed separately of the most identifiable parts of Jolanta, and ultimately her body as well.
"I think they must have been feeling pretty confident."