Obama's next big choice: Who should run the Joint Chiefs of Staff?

President Obama's formal unveiling of his retooled national-security team still leaves one key job open: the chairmanship of the Joint Chiefs of the Staff. The current occupant, Adm. Mike Mullen, retires this fall.

Obama's decision to name CIA Director Leon Panetta as the next Defense secretary and to bring Gen. David Petraeus home from Afghanistan to replace Panetta at the CIA lifts much of the uncertainty that has hung over both places for months.

But the moves will set off a heated game of musical chairs within the military, as an array of top posts start to come open in the months ahead. In addition to picking Mullen's replacement, Obama will also need to choose a vice chairman of the Joint Chiefs of Staff and a chief of naval operations.

The upshot is that the administration's reshaping of the Pentagon is far from complete. By October, Obama will need to replace half the Joint Chiefs of Staff and several high-profile regional commanders. That means the upper ranks of the armed forces will be in a state of flux just as the administration makes a series of pivotal decisions about the way forward in Afghanistan, Pakistan, Iraq, and Libya.

Petraeus had long been seen as a potential successor for Mullen, who is scheduled to step aside in October, and his move to the CIA means that attention will now shift to a different and far less well-known group of candidates. With Gates set to retire on June 30, Panetta's first major decision at the Pentagon will be to advise Obama on whom he wants at his side as the nation's top military officer.

The front-runner for the job is Marine Gen. James Cartwright, the vice chairman of the Joint Chiefs of Staff, who impressed Obama and other top administration officials during last year's strategy review about the flagging Afghan war. The other top contender is Adm. James Stavridis, who commands NATO and all U.S. forces in Europe and is widely respected in military circles for his keen intellect and diplomatic savvy.

The coming personnel choices could be difficult ones for the president, who has little time in which to make the decisions. Cartwright's term ends in August, the next naval chief has to be in place in September, and Mullen will retire in October. Panetta won't assume the helm of the Pentagon until July 1 at the earliest, which means that he and Obama will have to almost immediately start making key decisions about who will fill each of the posts.

Complicating matters further is that several of the officers are in the running for multiple posts at the same time. Stavridis, for instance, is also a leading candidate to succeed Adm. Gary Roughhead as chief of naval operations. Because that job will need to filled before Mullen's replacement is named, Obama's choice of the Navy's next top officer could narrow the field of candidates for the chairmanship of the Joint Chiefs of Staff as well.

Beyond the Joint Chiefs of Staff, the coming personnel shifts will open up an array of other senior posts at top regional commands. Regardless of which post he gets, the administration will soon need to pick an officer to replace Stavridis, the commander of NATO's armed forces and the administration's primary envoy to the civilian leadership of the fractious military alliance. The job is likely to grow in both importance and difficulty in the years ahead because of growing tensions between Washington and its allies over NATO's contributions to the war effort in Afghanistan and the ongoing military intervention in Libya.

The White House also needs to pick a deputy commander of Central Command, which oversees the wars in Afghanistan and Iraq. Lt. Gen. John Allen, who holds the post, will move to Kabul this fall to replace Petraeus. The music is just starting to play, and there are lots of chairs to fill.