The remaining thirty are expected to leave the hospital Friday and through the weekend.
Hundreds of well-wishers had gathered outside the entrance of the hospital to greet them, but the three men managed to slip out through a side door.
The miners haven't talked much publicly about their 69 days underground. They have reportedly told family members not to talk with reporters without their permission.
The daughter of one of them said the men have agreed to share all their earnings from interviews, media appearances, movies or books.
One of the 33 miners said he doesn't want to be famous. He said he just wants to make sure the men's experience motivates the mining industry to improve worker safety so that something similar doesn't happen again.
The Associated Press Contributed to this report.