WASHINGTON — The hottest game in town for U.S. defense insiders is trying to figure out who is going to get the top jobs once Defense Secretary Robert Gates steps down this summer and Adm. Michael Mullen, the chairman of the Joint Chiefs of Staff, retires in October. Gates has not publicly announced exactly when he will leave, but observers and insiders expect he will exit in late summer or early fall, after the administration’s Afghanistan review wraps up in July.

Many of the candidates once thought to be front-runners for the posts have faded. According to their spokesmen, Secretary of State Hillary Clinton and former Deputy Defense Secretary John Hamre, now the president of the Center for Strategic and International Studies, are staying in their current jobs.

And the original leading candidate for chairman, Marine Corps Gen. James “Hoss” Cartwright, the vice chairman of the Joint Chiefs of Staff, remains the administration’s favorite, but it is unclear if he will face confirmation problems in the wake of an inspector general investigation. Cartwright was investigated in 2009 for allegations of an improper relationship with a female subordinate.

Although Cartwright was cleared of having an inappropriate relationship, he was criticized for showing poor judgment in the case. Sources say the taint of an investigation makes for a potentially risky and embarrassing confirmation process should lawmakers question him about the matter during confirmation hearings.

If not promoted, Cartwright is expected to retire as soon as Aug. 31, opening yet another position for the administration to fill.

The administration has just a few weeks to make its picks if they are to be confirmed by summertime. The Federal Bureau of Investigation takes six weeks to vet potential nominees in excruciating detail. Once scrubbed, the nominees will be named and sent to the Senate Armed Services Committee for confirmation.

Here is a look at some candidates for the top jobs.

Defense Secretary

  • CIA Director Leon Panetta. A savvy operator with gravitas and toughness, Panetta is a former congressman with strong budget experience who ran the White House Office of Management and Budget during the Clinton administration and later became White House chief of staff. Those skills will come in handy should the Pentagon face budget cuts.

But the Obama administration may be loath to seek a new spy­master during ongoing reforms at the CIA. And some question whether Panetta, 72, is a tad old for the top job in the Defense Department (DoD), which has long been regarded as the most grueling in the Cabinet — especially in wartime. It’s an 18-hour-a-day, 6.5-day-a­week gig, and after five years in the job, Gates, 67, is said to be exhausted. Plus, the CIA is a much smaller organization and is subject to less public scrutiny.

If Panetta were to switch jobs, news reports for weeks have suggested Army Gen. David Petraeus, the commander of multinational forces in Afghanistan, as one potential replacement.

  • Navy Secretary Ray Mabus. A former Mississippi governor and ambassador to Saudi Arabia, Mabus has led the Navy since June 2009. Aside from being smart and politically savvy, he is close to the president and fiercely loyal to the administration, which prompted Obama to tap Mabus to craft a long-term recovery plan for the BP Gulf Coast oil spill last year.

During a House Armed Services Committee hearing last month, Gates gave Mabus an unsolicited pat on the back for his work on energy initiatives. Mabus’ name also has been tossed around for commerce secretary. Still, he is considered a long shot for SECDEF.

The top candidate to replace Mabus is Juan Garcia, the assistant secretary of the Navy for manpower and reserve affairs, who is seen as one of the Pentagon’s dynamic young leaders. It also does not hurt that he is a law school buddy of the president’s.

  • Ashton Carter, undersecretary of defense for acquisition, technology and logistics, is regarded as one of the Pentagon’s bright stars. He is thought to be in line for deputy defense secretary and, later, for the top job itself.

Carter has a reputation for smarts, innovative thinking, pragmatism and a network of connections from the White House and beyond. He has been on a quest to reform the Pentagon’s weapons buying policies, hold contractors responsible for shoddy work and get the DoD more bang for its buck.

A former Harvard professor, Carter also has served on a range of international advisory and policy review boards, giving him a global Rolodex.

Those who have said they are not interested in the job include:

  • Sen. Jack Reed (D-R.I.), long been mentioned for the top job, is happy in the Senate. And after losing the House in the midterm elections, the Obama administration is not eager to take any chance of losing any more seats in the Senate.
  • Colin Powell, former chairman secretary of state and national security adviser, has told friends he would not take the job. But as with Hamre, insiders say that if asked by the president, Powell would find it hard to refuse.

Joint Chiefs of Staff Chairman

As for who will replace Mullen, the jury is still out. The top issues for the White House in this selection, sources said, are candidates whom the administration has worked with comfortably and developed a trusting relationship. And with the nation now in three wars, combat experience has emerged as a big plus.

The outlook for candidates aside from Cartwright, however, is cloudy.

  • Army Gen. David Petraeus has the credibility to take the top job, but it is unclear the administration is ready to offer it to him.

Petraeus cleaned up Iraq and set the wheels in motion for an eventual U.S. troop withdrawal, then took a demotion from the head of U.S. Central Command to lead a troop surge in Afghanistan. Sources have long said that if he does not become chairman, Petraeus would take the top U.S. job in Europe as chief of the European Command and NATO’s Supreme Allied Commander Europe.

But Petraeus has not had the smoothest relationship with the White House. As detailed in Bob Woodward’s book, “Obama’s War,” during the course of its Afghanistan war review the administration grew frustrated with the four-star general who they felt used his supporters to get more troops for the mission than the White House wanted to authorize.

But after firing Army Gen. Stanley McChrystal from the top post in Afghanistan, the White House turned to Petraeus as a replacement, and sources say his stock has risen with the president.

Can the White House risk selecting a chairman who has major political clout and a reputation for using his media allies to get what he wants? Or can the administration afford not to tap America’s most famous, admired and battle-experienced general to lead the nation’s military? If he does not become chairman or CIA director, Petraeus has long been said to covet the Supreme Allied Commander Europe post.

Marine Lt. Gen. John Allen, the deputy commander of the U.S. Central Command, is seen as the front-runner to replace Petraeus in Afghanistan.

  • Navy Adm. James Stavridis, the first sailor to head European Command and Supreme Allied Commander Europe, was seen as a chairman contender, but is more likely to relieve Adm. Gary Roughead as the chief of naval operations later this year.

Stavridis is regarded as one of the military’s most innovative and articulate thinkers, but has spent the past eight years in joint assignments, first leading U.S. Southern Command, then reporting to European Command. He is credited with helping convince reluctant European governments to keep coughing up troops for the mission in Afghanistan. Given the strategic and budget challenges ahead, his brand of “big think” would be valuable, one general said.

If Stavridis becomes chairman, then some see Adm. Jonathan Greenert, the vice chief of naval operations, to fleet up to the top job.

  • Navy Adm. Robert Willard, the head of U.S. Pacific Command, has been mentioned as a possible chairman, given his experience in Asia.

The Obama administration has been increasing engagement in the region, and Willard has played a key role to both reassure allies and, when needed, challenge China. This helped make him a rising star who has gained even more prominence thanks to his oversight of relief operations following the earthquake and tsunami last month in Japan.

  • Army Gen. Raymond Odierno, now the chief of the soon-to­disappear U.S. Joint Forces Command (JFCOM), is another strong candidate for either of the top uniformed jobs.

A tough, hard-driving combat veteran, Odierno got the ball rolling on troop withdrawals from Iraq after taking the reins from Petraeus, and now is shutting down JFCOM, a move highly unpopular in Virginia, the home of the command.

But if Petraeus becomes the chairman, Odierno is out; the chairman and the vice traditionally represent different services. He would bring recent combat experience to the top ranks of the military leadership.

Joint Chiefs of Staff Vice Chairman

Among those who might replace Cartwright as vice chairman are:

  • Gen. Norton Schwartz, the Air Force chief of staff. Schwartz was first mentioned as a possible vice chief about a year ago when Cartwright was seen as a possible successor to Jim Jones as national security adviser. When Tom Donilon replaced Jones, a former Marine general who served as commandant, Cartwright stayed put at the Pentagon, and with Schwartz not fleeting up to the new post, other top Air Force officers quickly announced their retirement.

Schwartz had planned to retire nearly three years ago when Gates asked him to take over the Air Force after his predecessor was fired. Since then, he has worked to reshape the Air Force’s culture to adapt more toward the irregular warfare missions like the ones seen in Afghanistan while also preparing for more high-intensity future conflicts.

He has held his subordinates accountable for their actions and pushed joint service warfighting concepts, particularly with the Navy. Schwartz has previously served as the director of operations and director of the Joint Staff.

In a key plus, Schwartz has strong programming and budget experience — which Odierno lacks — that will be critical in fiscally constrained times.

Should Schwartz be promoted, possible replacements include Gen. Gary North, the chief of Pacific Air Forces, and Gen. William Fraser, the chief of the service’s Air Combat Command.