Iraq--Go After the Clerics

From what I have read in the Koran killing of innocents is not justified--a fact admitted by Islamic radicals themselves. Radical clerics are haranguing their flocks daily to go out and kill infidels--particularly Americans, British, and Israelis. Politics, religion, and hate is a witches brew that requires strong medicine to excise.
The only logical recourse left is to go after those clerics who promote hate and violence; removing the head of the snake, so to speak.
Not to do so is to accept the status quo of continued attacks on our troops and innocent Iraqis. We could expect some uproar from our enemies but removing radical clerics would have a profound long term positive effect; by reducing the numbers of terrorist recruits.