Mohamed Alessa and Carlos Almonte were sentenced April 15, around the time of the bombings.
The two were arrested in 2010 and pleaded guilty to conspiring to join an armed Islamic group in Somalia with ties to al-Qaida.
Defense attorneys filed a joint motion Monday asking to have Alessa's 22-year sentence, and Almonte's 20-year sentence, reconsidered.
The judge denied an earlier defense claim that he had received a note about the bombings during the proceedings. The judge said the note related to his wife.
Federal prosecutors reiterated the judge's claim that the sentence had nothing to do with the Boston bombings.