Tariq Aziz: Even his status is in question
While the United States vigorously searches for former members of the Iraqi regime, it still has not decided what to do with those it has caught.
One thing is certain. The Americans will not send them to the International Criminal Court or set up any new international tribunal.
That is something to which the Bush administration is ideologically opposed.
Instead, US officials have said that American military or civilian courts will deal with those accused of crimes against American citizens.
That would cover mostly war crimes, but it is unlikely to apply to civilian leaders like Tariq Aziz.
The US has not even decided whether he is a prisoner of war or not. Technically he is just in custody and being questioned for information.
The official policy is that the US will help set up new Iraqi courts to try leaders accused of crimes against their own people.
That has already brought loud protests, not just from human rights groups, but from members of Congress.
Leading Democratic Senator Joe Biden said recently that it would be a tragic mistake for the US not to set up an international court.
The other question is where to hold suspects.
There are still hundreds of detainees from the Afghan conflict at the American base at Guantanamo Bay, Cuba - but few Iraqi prisoners of war are likely to be sent there.
In fact, according to the Geneva Convention, most prisoners of war should be released at the end of the conflict, but at the moment the Bush administration is still feeling its way through this complicated legal situation.