But Wednesday’s hearing was instead told that his lawyers had “abandoned the primary argument” that Bravery should have been given a hospital order instead of jail sentence.
The teenager was jailed for life with a minimum term of 15 years in June, after admitting an attempted murder charge, and is appealing to reduce the sentence.
He threw a six-year-old boy, who was a French tourist on holiday with his parents, off the Tate Modern’s 10th floor viewing platform on 4 August last year.
Bravery, then 17, was seen backing away from the railings while smiling and appearing to laugh immediately afterwards.
The boy fell five storeys before landing on a roof, and was left with life-changing injuries. It is not known whether he will make a full recovery.
When challenged by the victim’s father, Bravery told him he was “mad” and witnesses described him having a “big smile on his face”.
Representing Bravery Pippa McAtasney QC told the Court of Appeal that a clinician at Broadmoor hospital had originally said Bravery should have been given a hospital order with restrictions.
She added: “I have received an update from [the doctor] only last week and a report has been made available ... where she has, for a proper reason, changed her expert opinion based primarily on the fact that Mr Bravery appears to have settled into the regime at Belmarsh prison.”
Ms McAtasney argued that the 15-year minimum term handed to Bravery by Mrs Justice McGowan at the Old Bailey was too high.
She said a greater discount should been given for factors including Bravery's mental health, including his autism diagnosis, and his age.
The barrister told the court: “Taking into account all his mental health presentation, his age and lack of maturity and vulnerability, the figure that the learned sentencing judge discounted for all of those pieces of mitigation should have been greater than five years, in my submission.”
Deanna Heer, representing the Crown, argued that Bravery's sentence was not “manifestly excessive”.
“The act of throwing a six-year-old child over the balcony ... in full view of his parents and the public can, in my submission, only be accurately described as an offence of exceptional callousness for which the culpability must be extremely high,” she told the court.
"He intended to kill, he had planned the killing and researched the most effective way to carry out the killing, narrowing it down to three possibilities: strangulation, drowning or doing what he did.
“Having decided upon a method, he deliberately selected a vulnerable victim — a child who, as he said, would be unable to stop him.”
Bravery was in supported accommodation under the care of Hammersmith and Fulham social services at the time of the attack, and had been allowed out unsupervised despite a history of lashing out at staff.
Ms Heer said: "He deceived his carers about his whereabouts that day, making his way to the Shard initially and eventually to the Tate and then, in the aftermath of the act, expressed disappointment that he had failed to kill the child."
She described the attempted murder as “a strategic act of violence” which had caused ”profoundly life-changing injuries“ to the victim.
The appeal is being heard by Dame Victoria Sharp, president of the Queen's Bench Division, sitting with Mr Justice Edis and Mrs Justice Yip at the Royal Courts of Justice in London.
Additional reporting by PA