The two cases are all that lie between justices and a three-month vacation from the court.
Initially, the court had planned to adjourn for the summer on Monday, but the justices had not finished work on five cases.
On Wednesday they ruled in a Texas redistricting case and cases involving the rights of inmates and foreign suspects.
At the end of Wednesday's session, Chief Justice John Roberts announced that the high court would finish its work on Thursday.
In the two remaining cases, the justices will decide:
—Whether President Bush overstepped his authority with military war-crimes trials for foreigners held at the U.S. prison camp at Guantanamo Bay, Cuba.
—Whether to strike down Arizona's insanity defense law, in an appeal brought on behalf of a schizophrenic teenager who killed a police officer.