house of correction

from The American Heritage® Dictionary of the English Language, 5th Edition.

• noun An institution for the confinement of persons convicted of minor criminal offenses.
• noun An institution dedicated to the management and rehabilitation of persons perceived to be at risk of becoming criminals.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

• noun A residential penitentiary facility, an institution where criminals or wayward people (notably youth) are sent to have their ways 'corrected' trough a penal regime officially intended to reeducate them

from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.

• noun (formerly) a jail or other place of detention for persons convicted of minor offences