According to the latest draft of the Iraqi constitution (with thanks: Lily), an earlier clause denying dual nationality to Jews who left after 1968 and who are now Israelis seems to have been scrapped. (These lucky few thousand, like all refugees from the post-68 Ba'ath regime, have also been allowed to claim compensation for their lost property.) However, the vast majority of Iraqi-Israelis, who left in the early 1950s, would still not be allowed to regain their lost Iraqi citizenship.
It is certainly bizarre that Iraqi Jews have been allowed to vote in the Iraqi elections, but not to claim citizenship.
Anyone interested in a general analysis of the constitutional drafting process can find it here.
This current draft—like the earlier one— contains errors ( the date February 8 should have probably read July) and is still very much a work in progress. The deadline for the Iraqi constitution's final draft is 15 August. Here is the article as it now stands:
4. An Iraqi is allowed to bear more than one citizenship. An Iraqi who was stripped of his citizenship after February 8, 1968 for any reason is considered Iraqi and is entitled to regain [his citizenship].
The earlier draft of 30 June, which was featured in the Iraqi newspaper Al-Mada, took pains to exclude Israelis from those who could obtain dual citizenship: (The main purpose of this clause is to deal with the Shi'a and some Kurds who lost citizenship in the 1970s.)
"3. Any individual with another nationality (except for Israel) may obtain Iraqi nationality after a period of residency inside the borders of Iraq of not less than ten years for an Arab or twenty years for any other nationality, as long as he has good character and behavior, and has no criminal judgment against him from the Iraqi authorities during