Former U.S. Rep. William Jefferson (D-La.) stands outside the federal courthouse in Alexandria, Va., with his wife, Andrea, in August 2009 after being convicted of 11 fraud and bribery charges. (Kevin Wolf/AP)

Federal prosecutors have agreed that former congressman William Jefferson should not serve any more prison time now that parts of his corruption conviction have been overturned.

Jefferson, 70, a Democrat from Louisiana, was convicted on 11 fraud and bribery charges in 2009. But seven of 10 remaining convictions were overturned by a judge earlier this year in light of the Supreme Court's ruling in the case of former Virginia governor Robert F. McDonnell (R). One conviction was overturned by an appeals court in 2012.

The judge, T.S. Ellis III, released Jefferson from prison pending resentencing on the remaining counts.

At a hearing Friday in U.S. District Court in Alexandria, Va., the government will agree that Jefferson should be sentenced to the time in prison he has already served — more than five years, attorneys said in a joint court filing Thursday.

His initial sentence was 13 years.

Prosecutors will also not push for any supervised release, according to the agreement. The judge is not bound by the agreement and could sentence Jefferson to further imprisonment.

Jefferson is most famous for stashing $90,000 in cash in his freezer, which the government said was intended as a foreign bribe. He was found guilty of taking over $400,000 in bribes for helping to arrange business deals in Africa.

But Ellis ruled that the Supreme Court's definition of "official acts" meant most of Jefferson's behavior was not criminal.