Instead, "Black Widower" Malcolm Webster simply repeated his denial that he murdered nurse Claire Morris, 32, who died in a fireball crash on a lonely road near Kingoodie, Aberdeenshire in 1994.
He also denies attempting to murder New Zealander Felicity Drumm in a similar insurance scam in 1999.
Judges had expected to hear Webster, 54, to try to convince them his 30-year minimum sentence was too harsh.
But defence QC Gary Allan said Webster had instructed him not to put forward any argument - because it might make it look as though he were guilty.
Lord Eassie sitting with Lady Clark and Lord Wheatley allowed Webster to drop his attempt to cut his sentence.
Mr Allan told the Court of Criminal Appeal in Edinburgh: "Mr Webster has consistently and vehemently denied his guilt of the crimes.
"His position remains entirely unchanged. He maintains he did not commit the crimes and the verdicts of the jury represent a gross miscarriage of justice."
Webster has already lost an appeal against conviction but could still try to persuade the Scottish Criminal Cases Review Commission - which looks at possible miscarriages of justice - to listen to him.
Webster hoped huge insurance pay-outs and property left to him in his victims' wills would enable him to live a life of luxury.
But his days of top-of-the range cars, ocean-going yachts and designer clothes ended with a marathon trial in 2011 and a life sentence.
It took 17 years for justice to catch up with Webster.
Lord Bannatyne described his crimes as "utterly appalling" and said the murder of Claire Morris was "cold blooded, brutal and callous".
Her family said they were pleased that her killer had dropped the appeal.
Peter Morris, the brother of Webster's first wife, said he believed the evil nurse would continue to appeal through other courts.
Mr Morris said: "He obviously wants to continue an appeal in the Supreme Court or a European court because he just wants to drag it out.
"He's delusional. He has no feelings for other people, he doesn't want anyone to have any closure because he maintains his stance of innocence.
"How long do we listen to someone who keeps standing there and despite all of the proof and evidence, keeps saying that they are innocent?
"It's ridiculous really."
He added: "Ultimately I'm pleased that the sentence is upstanding.
"As far as I'm concerned there is no cure for someone who is a psychopath so he probably should have a whole life sentence really.
"He would still be dangerous after 30 years."