Doctors treating 30 freed miners still in hospital in Chile say at least 10 of them will be discharged on Friday.
Three of the men were allowed home on Thursday and officials at the hospital in the northern town of Copiapo say the rest are in "very good shape".
One of the men discharged from hospital, Edison Pena, has expressed his anger about the accident.
"Why do these things have to happen? Because the employer wants to make money," he said.
He said that when they were trapped he thought they were going to die.
Mr Pena, Juan Illanes and Bolivian Carlos Mamani were greeted by cheering neighbours as they arrived home.
They had been allowed out of hospital the day after they were rescued from the San Jose mine after spending 69 days underground.
Health Minister Jaime Manalich told reporters that all 33 men were likely to have a hard time psychologically.
None has given a detailed account of their time trapped in the mine, but Juan Illanes described the first 17 days of the ordeal as a nightmare, before they were discovered by rescue workers.
He later told reporters that he needed to be alone and quiet.
No details have been given of the men who will next be given permission to leave hospital but Mr Manalich said all 30 were in good condition, despite problems that many have had with their eyes and teeth.
Mario Gomez, the eldest of the miners at 63, is on a course of antibiotics for acute pneumonia and the health minister said he, too, was doing well.
'A new life'
Mr Manalich said the miners would all be closely monitored over the next six months and he predicted that tough times lay ahead of them.
"They have to adapt to a new life. Therefore we are prepared to stay with them and to work at least in the next six months," he said.
He told a news conference that one of the miners had told him how he had gone to sleep on Thursday night and woke up an hour later with a jolt, thinking he was still in the mine.
A measure of the concern the miners have for their future has been revealed by Edison Pena, who told reporters outside his home in Copiapo that he would like to use his experience as an example to motivate others.
"But I'm afraid in three months, when the interviews are over, it may be difficult for me and my colleagues to find a job. I may end up selling sweets in the town square," he said.
The government has promised the men it will help find them new jobs although their salaries are only due to be paid for another month.
As Chileans continued to celebrate the extraordinary rescue of the 33 San Jose miners, there was a reminder from Ecuador of the dangers of working in mines.
Officials said four miners had become trapped 150m (490ft) underground when part of a gold mine collapsed in a southern coastal region near the Peruvian border.
One of the workers managed to escape and alerted the authorities.