Petraeus’s 15-month tenure as CIA director was short and, compared to his rocket-like ascent to four-star rank in the Army, something of a bumpy ride. He was a man who was used to a large staff that executed his orders, and what he found at the CIA was something closer to a covert university campus, with experts who behaved as if they had tenure, and a culture that prided itself on being contrarian and difficult to manage.

It wasn’t an easy fit, and within weeks, you began to hear grumbling from the CIA’s ranks about how Petraeus was trying to put his personal mark on every tree and fire hydrant in sight, asking too many questions, and pushing in his annoyingly relentless way for results.

The smartest thing Petraeus did was to form a partnership early on with Michael Morell, who was acting director before his arrival and resumed that role Friday. Morell is a career analyst and veteran of the mill that produces the famous “PDB,” or president’s daily brief, and he knew the agency’s culture — or at least the analysts’ version of it. His task was to encourage Petraeus when his commander’s instincts made sense for the agency, and dissuade him when his ideas were counter-productive.

Petraeus’s critics within the agency think Morell was co-opted by Petraeus. But there’s considerable evidence that, when appropriate, the deputy director was prepared to tell the boss the unpleasant truth. In any event, Morell came away a fan—recognizing that although Petraeus had a rocky start, his ceaseless pressure had been good for the agency.

“Petraeus is one of the best managers I have seen,” Morell said through a spokesman Friday.  “He figures out where he wants the organization to go, and he drives it in that direction.  He does this through relentless focus.  He remembers what he asked for. Three weeks later he’ll say at the morning meeting, ‘Whatever happened to that?  Is that done yet?’  I’ve never seen anyone with his drive — ever.”

Not that it was easy. “This place does not like hierarchy. People respect you because you do a job well, not because you’re the director,” observed one senior agency official. Petraeus had gone from “an organization trained to salute to one that was like herding cats,” another official said Friday, and it was “a huge transition for both sides.”

The transition was complicated by the fact that Petraeus was moving from being the most visible and celebrated general in modern American history to operating in the shadows, away fromthe TV cameras and the journalists he had courted as a military officer. This reticence was at the insistence of the Obama White House, which gave Petraeus the CIA job despite deep worries about whether he would be a team player and stay out of the limelight.

Petraeus wasn’t entirely happy with his new invisibility — rightly reckoning that he was one of the more effective communicators of his generation when it came to global strategy. But he accepted his new obscurity as the price of the new job, and over time, he seemed to become more comfortable with it. A more visible and public role, as president of a university or secretary of state, was tempting, in part because it would allow Petraeus to play on all the strings. But until Friday, he seemed likely to remain at the CIA, at least into the new year.

What Petraeus has always done best, in the military and at the CIA, is pushing at the edges of what people assume is possible. When he took over command of U.S. forces in Iraq in 2007, most of the U.S. military leadership had given up on the war and wanted out. Petraeus had spent several years thinking about couner-insurgency strategy after his two-star stint as head of training of the Iraqi army. So when President Bush decided he wanted to fight on in Iraq for a more decent withdrawal, Petraeus was armed and ready with a strategy.

But it wasn’t the counter-insurgency doctrine that made the difference in Iraq. It was the force of Petraeus’s will. With an inner circle of close advisers, he bent the history of that war around his personality, in the years he was commander. He also made some mistakes, in my judgment, especially in over-relying on Prime Minister Nouri al-Maliki — a mistake that was repeated by the Obama administration.

Petraeus next became Centcom commander, where he roamed across the post-9/11 battlefields of the Middle East. I spent nearly three weeks traveling with him during his Centcom assignment, and I saw how he fused the political and military aspects of command, as he met with sheiks and presidents and intelligence chiefs, in a way that should have been captured in a textbook for future commanders.

The final military job was probably the hardest, as commander of U.S. forces in Afghanistan. For all Petraeus’s counter-insurgency doctrine, that command often appeared to be the equivalent of building on quicksand. No sooner were the Afghan forces “stood up” than they would begin to slip away, back into the culture that was deeply, stubbornly resistant to outside pressure. In his last month in Kabul, Petraeus had all the tools of victory in hand except one—the Afghan people and institutions.

In every job he had over the past decade, Petraeus liked to ask: “What’s the big idea here?” It was his way of getting to the intellectual center of a problem. And he used that same approach at the CIA, as he explained in a speech on Sept. 10.

As I see it, strategic leadership is fundamentally about big ideas, and, in particular, about four tasks connected with big ideas.  First, of course, you have to get the big ideas right—you have to determine the right overarching concepts and intellectual underpinnings to accomplish your organization’s mission.  Second, you have to communicate the big ideas effectively through the breadth and depth of the organization.  Third, you have to oversee the implementation of the big ideas.  And fourth, and finally, you have to capture lessons from the implementation of the big ideas, so that you can refine the overarching concepts and repeat the overall process.

Petraeus went on in that Sept. 10 speech to explain why the CIA job was different: "My leadership style at the CIA, for example, is far different from the style I employed in the early 1990s as an air assault infantry battalion commander.  Though I do chart an azimuth, establish goals in consultation with our other key leaders, determine left and right limits, and lay down markers to guide the organization, the CIA — thanks to its seasoned and highly educated work force — does not need a heavy hand on the reins.  A light touch is generally all that is required."

Petraeus didn’t always follow that advice, certainly in his personal life. But it’s still interesting to ask the same question people have been posing about him for more than a decade: What’s the next chapter?”