As part of a plan put to the Iraqi government in December, US authorities aim to close Bucca in September, after the overall detainee population drops below 8,000.
Taji is due to be handed over to local control in early 2010, and Cropper is set to follow in August the same year.
The Iraqis being transferred are all sent to prisons that are regularly inspected by American authorities.
Gen Quantock said the United States had increased oversight, and now invites 'anybody who wants to come and see how we do detainee operations to come to our facilities.' All of the prisons inspected and approved by US teams are run by the justice ministry - Iraq's fractured prison system means the ministries of justice, defence and interior all operate their own facilities.
However, in the wake of the June 30 pullback from Iraqi towns and cities, pullback from Iraqi towns and cities, Gen Quantock emphasised he did not want progress made in detainee operations to be lost when the US military leaves the country for good at the end of 2011.