The government is changing the terms of its bailout agreement with Fannie Mae and Freddie Mac in a way that will shrink the holdings of the two mortgage giants more quickly and will require payment to the government of all quarterly profits the companies earn.

The Treasury Department announced the changes Friday in an effort to deal with concerns that the companies could at some point exhaust the federal support they were guaranteed when they were taken over by the government in September 2008 during the financial crisis.