Admiral Mike Mullen, who just returned from Iraq, told reporters at the Pentagon that he found conditions improved there.
The top U.S. military commander in Iraq, General David Petraeus, will take the next six weeks to decide how many personnel can be brought home.
The trrop surge has now ended, but there are still 150,000 U.S. forces in Iraq, 15,000 more than before the build-up began.
