By Jonathan Marcus
BBC diplomatic correspondent
The announcement by interim Iraqi Prime Minister Iyad Alawi that some of Saddam Hussein's leading associates could face trial as early as next week will please both opponents and victims of the Baathist regime.
Thousands of people disappeared during Saddam's rule
But many international legal experts are concerned that, however serious the charges against them, the conditions have not been created to enable these people to have anything resembling a fair trial.
The crimes committed by Saddam Hussein's regime in Iraq are horrific.
Opponents of the government were murdered, women raped and whole areas of the country subjected to brutal military assaults, including the use of chemical weapons.
While many mass graves have been identified, nobody can yet give an accurate figure of how many people died.
Seeing justice done
Putting the leaders of the Baathist regime in Iraq on trial has been a key aim - not just for the US, but for the interim Iraqi government itself.
There is a feeling that with a full reckoning of the previous regime's crimes, the new government's legitimacy will be enhanced.
The trials will thus perform a useful public purpose.
The former Iraqi leader has already appeared in court
But for justice to be done, the trials must also be fair.
And international legal experts have raised serious concerns about what they see as a rush to judgement.
Most, if not all, of the accused have only appeared before Iraq's central criminal court, not the special tribunal charged with hearing the cases of former regime members.
Many of the accused complain that they have not had access to legal representation.
And Richard Dicker of Human Rights Watch says that "bringing the accused to trial without formal indictments or defence lawyers being allowed to properly prepare their cases suggests an objective other than justice".
The implication is that there is a political dimension here linked to the forthcoming Iraqi elections, although if trials do begin next week - and that is far from certain - they could well take a very long time.
And there is a clear desire to secure some initial convictions before Saddam Hussein himself has his day in court.