A manslaughter confession from wife-killer Borce Ristevski has averted the need for a high-profile murder trial and despite previously gunning for a murder charge, police are satisfied.
Chief Commissioner Graham Ashton said Ristevski's plea would allow "justice to move through the courts more quickly".
"Certainly for people required to give evidence and other members of the family ... it speeds up the process and it's all part of that bargaining, that plea situation, that is dealt with as a matter of course," he told ABC radio on Thursday.
"(I'm) not disappointed. Everyone worked very hard on that case. The police ... will be sort of relieved in a way too they will be able to move through with that plea."
Ristevski, 55, pleaded guilty on Wednesday to the manslaughter of his wife Karen almost three years after she went missing in June 2016.
The admission was made on the eve of a scheduled five-week murder trial.
Supreme Court Justice Christopher Beale ruled Ristevski's actions after the killing - when he played the role of grieving husband - could not be used to prove "murderous intent".
Prosecutors subsequently filed a new indictment with the lesser charge of manslaughter, which Ristevski admitted, scuttling the murder trial.
The killer's son from a previous marriage, Anthony Rickard, said his father pleaded guilty to avoid details of his wife's relationship with his son.
"I gave him an ultimatum," Mr Rickard told news.com.au on Thursday.
"I told him 'If you don't get up and be a man I'll go into the (witness) box and tell them exactly what went on behind closed doors'."
Mr Rickard repeated earlier claims that he and his stepmother had a sexual relationship.
Last year, Mr Rickard was arrested for failing to answer bail and during a subsequent court appearance it was aired that he had been avoiding police ahead of his father's committal hearing.
Prosecutors had previously pushed hard for Ristevski to stand trial for murder, saying his deceitful behaviours after the killing gave rise to the required intent.
Mr Ashton said cases built on circumstantial evidence were always challenging rather than drawing on direct evidence.
"When you build those circumstantial cases, it can be a laborious and painstaking and often can in some cases come down to a jury accepting the circumstantial matters, proving beyond reasonable doubt that a certain set of facts has occurred," he said.
Ristevski was charged in December 2017 after a lengthy investigation that involved listening devices and CCTV footage analysis.
He allegedly killed his 47-year-old wife at their Avondale Heights home on June 29, 2016 and took her Mercedes-Benz roadster to dispose of the body in bushland.
Eight months later, her skeletal remains were found between logs in Macedon Regional Park.
Ristevski will face a pre-sentence hearing on March 27.