Two of the men are still in the hospital, but will be moved to another building shortly, said Paola Neumann, director of health services. She declined to say which of the miners would remain under doctors' care.

Some of the miners have had trouble sleeping, she said, but in general the men were making a better recovery than health officials had expected. None will require extensive medical treatment.

Three of the miners arrived late Thursday to joyous homecomings following their release from the hospital, CNN Chile reported. Officials hope that all 33, who have been mostly mum about their ordeal, will be home by Sunday, according to Neumann.

CNN's sister network, CNN Chile, identified the first three released as Juan Illanes, Edison Pena and Carlos Mamani. It aired video of several men and what appeared to be their families inside a red van departing the hospital grounds.

Their departure marked the beginning of the end of a frenzied joy that erupted Wednesday as the men were rescued.

The mine collapsed on August 5. The workers spent 17 days before they were able to establish their first contact with the outside world.

The miners spent Thursday meeting with President Sebastian Pinera and undergoing tests. All were reportedly in relatively good health.