Rob,
If you have the time, there are three books that talk in depth about the three primary sectors of Iraqi society (Sunni & Shi'a Arabs, and the Kurds) in the context that you are looking for.
The broadest (if you can only read one, this is the one) is A History of Iraq, by Charles Tripp. He takes a unique look at Iraqi history, by putting it in the context of the development of power bases, and the manipulation of support. If you are really pressed for time, get a hold of a copy and just read from Chapter 6 on - that covers the period under Saddam.
The other two are more narrowly focused: Agha, Sheikh and State, by Martin van Bruinessen, focuses on Iraqi Kurdish social structures. ("Sheikh" has a different meaning and context to the Kurds than it does to the Arabs.) If you work with the Kurds at all, I strongly recommend reading this one in its entirety.
The third and final volume is The Shi'is of Iraq, by Yitzhak Nakash. This is a very readable book with a tremendous amount of detail on Arab Shi'a history, culture and tradition. However, its over 200 pages of small print, so if you're not working with the Shi'a, it may not be worth the time invested...
Ted
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