The two Islamic fanatics found guilty of the murder of soldier Lee Rigby have had appeals rejected.
Michael Adebolajo's application for permission to appeal against his conviction was thrown out by Lord Chief Justice Lord Thomas and two other judges in London.
They also rejected Adebolajo's attempt to appeal against his whole-life sentence, which condemns him to die behind bars.
Lord Thomas, sitting with Lady Justice Hallett and Mr Justice Openshaw, also dismissed a sentence challenge by co-accused Michael Adebowale, who was jailed for life with a minimum term of 45 years.
The British-born Muslim converts ran 25-year-old Fusilier Rigby down in a car before hacking him to death with a meat cleaver and knives in a frenzied attack in Woolwich, south London.
Lord Thomas said their sentences were "just" punishment for the "horrific and barbaric" murder.
The pair had "gloried" in what they had done, he said.
Adebolajo's attempt to challenge his conviction was "misconceived" and "completely hopeless".
Members of Fusilier Rigby's family gasped with relief and there were tears in court as the decision was announced.
Adebowale watched the proceedings via video link from Broadmoor.
Adebolajo had waived his right to do the same from Frankland Prison, Country Durham.
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