Bradbury admitted 25 offences last September including sexual assault, voyeurism and possessing more than 16,000 indecent images while working at Addenbrooke's Hospital in Cambridge between 2009 and 2013.
He was initially jailed for 22 years by a judge at Cambridge Crown Court who told him his offences were a "gross and grotesque breach of trust".
Lady Justice Hallett, Mr Justice Haddon-Cave and Mr Justice Goss said they were "restructuring" his sentence and reducing it to 16 years with an additional six years on licence.
Bradbury's crimes were "wicked", said Lady Justice Hallett, who added that "a total figure of 22 years was appropriate".
But a "better way both to punish the appellant and protect the public" was to "restructure the sentence", she said.
At the time of trial it emerged that Bradbury, 41, classified himself as a 'devout Christian' and had been on a church mission to an African orphanage just days before he abused two young cancer patients.
He travelled with KingsGate Christian Evangelical Church from Peterborough, Cambridgeshire in 2012 to help children whose parents had died from Aids, as part of a 15-strong group that went to Swaziland to help orphaned children in 2012.
However a spokesperson for KingsGate told Premier he only attended the church for a limited time.
In a statement, the church said: "We are shocked and deeply saddened at the actions of Dr Myles Bradbury and at the devastating impact that these have had on the lives of many.
"As soon as the charges against him were revealed in early July 2014 we promptly contacted Bulembu.
"Bulembu then instituted a detailed investigation to make sure that he had not had any one-to-one contact with children during that time.
"They found no evidence that he had any unsupervised involvement with children and was always accompanied by community development project staff."