By MARK MOYAR

The firing of Gen. Stanley McChrystal has ended the career of an outstanding military leader and the only American to forge a close relationship in recent years with Afghan President Hamid Karzai. It has disrupted the war when the U.S. executive branch and Congress crave signs of immediate progress.

It has also brought in a new commander, Gen. David Petraeus, who has a great record and the public-relations savvy his predecessor lacked. Those assets, together with the urgency this crisis has given to longstanding problems, afford the new commander hitherto unavailable opportunities.

For one thing, the change may facilitate the appointment of an American ambassador who shares the strategic views of the military commander. Karl Eikenberry’s differences with Gen. McChrystal—and with Gen. Petraeus, who was on the same page as Gen. McChrystal—undermined efforts to organize militias and co-opt insurgents. Mr. Eikenberry’s contempt for Mr. Karzai has prevented him from accomplishing his most important mission—influencing the chief of state.

The selection of Gen. Petraeus will reassure our Afghan allies that the U.S. will not begin substantial troop reductions until the Afghans can handle the insurgents on their own. Cementing that reassurance, however, will require an explicit pledge from President Obama that he will withdraw troops only when conditions permit. Now would be an excellent moment for that pledge.

Last fall, Vice President Joe Biden and others contended that a large, unconditional troop withdrawal starting in July 2011 would convince the Afghan government to fight the insurgents more effectively. The president’s announcement of that date has had the opposite effect. Leaders in and out of the Afghan government—including Mr. Karzai—are now reluctant to combat the Taliban because they figure they’ll need Taliban assistance in the political and ethnic conflicts that will follow an American departure.

Gen. Petraeus’s appointment also presents an opportunity to make some changes in U.S. military personnel. Counterinsurgency is “leader-centric,” with the outcome dependent above all else on the quality of local leaders who conduct the security operations, organize good governance, and co-opt local elites. Some brigade and battalion commanders have performed these tasks poorly, but very few have been relieved of duty.

U.S. military leadership can also be improved through greater decentralization. Officers far removed from the field of battle have imposed undue constraints on counterinsurgency operations. Some junior officers have devised creative means of disregarding the constraints while appearing to abide by them, such as reclassifying operations so they do not fall under the regulations. Others have not, and have not been as effective in the fight.

The operation in Marja, once cited as a model for future battles, has failed to quash the insurgency because of the decision to focus on the population and not the enemy. The introduction of Afghan governance and large development projects, said Maj. Gen. Nick Carter, the NATO regional commander, would ensure that the population would support the counterinsurgency, thus preventing the insurgents from returning. Consequently, many insurgents were allowed to flee unmolested as the Marines prepared to move in.

The plan sounded great to academics and members of Congress, but it didn’t work. Insurgents who could have been killed at the beginning returned later to intimidate and kill civilians who participated in local government or aid projects, bringing those efforts to a standstill.

Gen. Petraeus will need to reappraise the plans for this fall’s crucial Kandahar campaign, because they are based on the same population-centric theory. “We’re not in the business of conducting an attritional campaign,” Gen. Carter said recently of Kandahar. “We’re . . . about bringing people into the tent and . . . using political levers to achieve that effect. So we will not be going head-to-head with insurgents in vineyards and orchards.”

Fortunately, Gen. Petraeus understands the need for both “population-centric” and “enemy-centric” operations. In Iraq he dedicated a large fraction of the “surge” troops to offensive operations aimed at the enemy, while others focused on population security, governance and development. The offensive operations succeeded in gaining the initiative, robbing the insurgents of sanctuaries and reducing their strength.

In Iraq, Gen. Petraeus’s implemented rules of engagement that reduced civilian casualties. But they gave more latitude to local commanders than the current rules in Afghanistan and they did not require as many time-consuming clearances. His Iraq experience will be invaluable in crafting new rules of engagement in Afghanistan.

Fewer restrictions on operations against the enemy will lead to higher civilian casualties because the enemy likes to take cover behind civilians. When President Karzai criticizes the U.S. for those casualties, Gen. Petraeus will have to apologize for mistakes, but he will also have to explain that the enemy’s tactics make civilian casualties inevitable. Citing his experiences in Iraq, he can show that effective employment of military force is required to win over fence-sitting elites, who want to back a winner.

Gen. McChrystal is turning over some noteworthy successes to Gen. Petraeus. For example, NATO officers have helped lead Afghan military and police forces that lack the officers to operate on their own, improving their performance markedly. A viable long-term strategy, however, requires development of Afghanistan’s own leadership capabilities. Gen. Petraeus can make major gains if he can induce Mr. Karzai and his cabinet to weed out poor commanders, as he did in Iraq in 2007 and 2008. Gen. McChrystal made considerable progress in reducing the influence of nepotism or cronyism in command selection; Gen. Petraeus can accelerate this progress if he has a new ambassador and a statement from Mr. Obama forswearing abandonment of Afghanistan.

The development of Afghan leadership has made impressive strides under Gen. McChrystal and Lt. Gen. William Caldwell, the commander of the NATO mission responsible for training Afghan security forces. Both men have acted to improve the quality of officer development, which was previously ignored in the rush to expand the enlisted ranks.

History shows that producing the battalion commanders and district police chiefs essential for success requires at least 10 years. The Afghan National Army has been under development for six. The Afghan National Police is just beginning real development. Regrettably, some in Washington still believe that we can produce the necessary officers in six months or a year.

Handing over the war to inexperienced Afghan officers in July 2011 will result in widespread desertion, defection and abuses of power that create new Taliban. Gen. Petraeus will need to drive home this point to all audiences in order to manage expectations. If anyone can convince the American public and political leaders of the need for prolonged involvement in Afghanistan, it is David Petraeus.

Mr. Moyar, the author of three books on counterinsurgency, will return to Afghanistan next month as research director of Orbis Operations, a counterinsurgency consulting firm.