We've learned the Cuyahoga County Jail is now holding Ariel Castro, 52, under what it calls "suicide precaution".
A spokesperson describes that as one step down from a "suicide watch".
Castro is facing charges for holding three women; Amanda Berry, Gina DeJesus, Michelle Knight and Amanda's six-year-old daughter, who was born in captivity, as hostages for years.
Police say he sexually abused the three women.
Castro went to the county jail Thursday morning after sitting in the city jail until his first court appearance.
The jail is holding Castro in his own cell being watched by a guard 24-7. That guard is watching in addition to the regular guard assigned to watch over that pod of cells.
A jail doctor evaluated Castro just after he arrived-standard practice for every inmate. He is described as "despondent".
We reported previously, Castro had been held by himself in the city jail, and he had been taunted and harassed by other inmates about the nature of his crimes.