What would Rome do? I think Rome would go in with 8-12 legions, take all Iraqi's as slaves and settle their retiring Legionaires in the province of Mesopatamia.
What wound Imperial Great Britian do? Go in with a small, highly technical army, kill the enemy leaders, and convince his 2nd in command to rule the whole country as a British client.
What would Alexander the Great do? Alexander would go in and marry a few muslim girls and force some of his greek soldiers to take muslim wives and promise that the children, a greco-iraqi mix would one day rule the world as conquerors. Then he'd get assassinated and all his plans would be undone.
And what does America do? We send a few advisors and drop a few bombs. Half-measures don't win wars. You want to pacify Iraq you need a draft and 200,000 american soldiers on the ground, and a willingness to see 2-3k dead every year. When you wage war, fight to win. If you can't afford to win, don't fight.
Those who thing my 200k idea is a good one should read Paul Kennedy's "Rise and Fall of the Great Powers" and learn what "Imperial Overextension" is. Then decide, is Iraq worth taking on more of that for the USA? Our Empire has some lifespan left in it. But it can't afford endless wars for little gain.