The Justice Department will begin considering clemency applications from nonviolent federal inmates who have behaved in prison, have no significant criminal history and have already served more than 10 years behind bars, according to a person familiar with the matter.

The initiative is part of a broader Obama administration effort to trim the nation’s prison population and ease sentencing disparities arising from drug possession crimes. The goal of the new criteria, which were to be detailed Wednesday, is to create a broader pool of eligible prisoners the Justice Department can recommend to the president to consider for shorter sentences.