Terrorist bombings and sectarian violence usually grab the headlines in Iraq. But the country is also experiencing deadly conflicts among its tribes—a very different type of violence. This deeply underreported phenomenon is unfolding particularly in the south of the country, often escalating into clashes that feature the use of heavy weapons.

Indeed, the free flow of arms in the hands of tribes is among the leading security issues in Iraq today. While many observers assert that quiet mediation is the key to successfully tackling tribal disputes...