Leaning on Iran has worked, as the Iran backed Shia group has announced that it does not intend to establish an Islamic Republic in Iraq. This, if nothing else, just recognizes reality. Most Iraqi Shias are not interested in having an Islamic Republic. It's been noted that the attempts to do that in Iran and Afghanistan have both failed.
U.S. troops captured General Hussam Mohammad Amin, head of Iraq's National Monitoring Directorate. This organization kept track of Iraq's military weapons and was the guy the UN weapons inspectors had to deal with. Amin was 49 on the list of "55 Most Wanted" by the coalition and would, obviously, know a lot about Iraqi efforts to hide forbidden weapons.