Customary International Law: What is its Role in the U.S. Legal System?

Customary international law is now coming up in a variety of contexts in U.S. courts, including civil suits under the Alien Tort Statute, the review of military commission proceedings in the "war on terror," and criminal prosecution of piracy. Is customary international law a form of federal law, as claimed by the Restatement (Third) of the Foreign Relations Law of the United States? How does its status in the U.S. legal system compare with the status of treaties? Even if it is not directly applicable as U.S. law, can customary international law inform the interpretation of federal statutes or certain constitutional provisions?