Alexander said a strategy devised by General Petraeus to work with local leaders and win them over to the U.S. cause has shown "clear success, province by province."
"They are fed up with random murders of their children" by al-Qaida terrorists, he said.
"There are probably seven provinces where enough progress has been made to involve Iraqis in their own security," claimed Alexander during the call with reporters.
Unmentioned in press accounts of Alexander and Corker's trip, however, is the fact that they only spent half a day on the ground in Iraq.
Read more on the senators' "fact-finding" tour at ThinkProgress.com.