The baby, seriously injured when his grandmother, Julie Ferne, died after falling three storeys in Vietnam while carrying him, is well enough for his father to return to New Zealand for Ms Ferne's funeral tomorrow.
Julie Ferne, 68, died last month after toppling over a railing and falling with Carter in her arms at her son's home in Ho Chi Minh City.
Baby Carter Preston was four-days-old at the time of the accident, and three weeks on is doing everything that a baby of his age does.
"There's actually reasonable hope he might well recover," Carter's uncle Stefan Preston said today.
Carter's mother, Chau, was now able to stay at the hospital with Carter and she could see him for half an hour every three hours.