If the country would be divided in Kurdistan, Shiitistan and Sunnitistan. Bagdad would be divided and the Oil fields. I think this would be a practical solution.
Then all that does is make religion a dividing point. Think about Nigeria and how they set up their state before Biafra seceded. They set it up so that each of the ethnic groups would be represented, thus making religion and ethnicity a dividing point even if people had the same interests at heart. What would happen if one of the countries thought they didn't have enough oil? They can use nationalism as a rallying call and start wars over it, just for more oil.