The latest draft Iraqi constitution has been approved by Parliament and will be voted on in a popular referendum in October. It has been criticised as long on aspiration, short on detail. There are lofty but vague declarations of equality and freedom of religion and affirmations of civil, personal and political rights.
As far as Jews wishing to reclaim their Iraqi nationality are concerned, the good news is that qualifyers in the previous drafts have been dropped. The bad news is that too much seems to have been left to the law to regulate.
Article (18): 1st - An Iraqi is anyone who has been born to an Iraqi father or an Iraqi mother.
2nd - Iraqi nationality is a right to all Iraqis and it is the basis of their citizenship.
3rd - (a) It shall be forbidden to withdraw the Iraqi citizenship from an Iraqi by birth for any reason. Those who have had their citizenship withdrawn have the right to reclaim it and this should be regulated by law.
(b)Iraqi citizenship should be withdrawn from naturalized citizens in cases stated by law.
4th - Every Iraqi has the right to carry more than one citizenship. Those who take a leading or high-level security position must give up any other citizenship. This shall be regulated by law.
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Update on the update: see this succinct analysis of the final draft constitution by Nathan Brown of the Carnegie Endowment (with thanks: iraqijews)