I’ve traveled extensively with Petraeus over the past six years in Iraq and Afghanistan. What stands out, beyond his extraordinary ambition and willpower, is his willingness to experiment — especially when the chips are down. In putting together the surge strategy, he gathered a team of iconoclasts — officers who were willing to think outside the box about what would work.

Creativity will be crucial in Afghanistan, where the strategy McChrystal devised is, frankly, spinning its wheels. I would bet that Petraeus will put more emphasis on bottom-up experiments. He’s good at working both sides of the street — placating presidents and prime ministers while he dickers with local militia leaders.

Petraeus is also an operator, in the sense that he likes to use back-channel emissaries to communicate with a wide range of players. That strategic edge has been missing in our Afghanistan policy, and it will become crucial next year, as we enter a likely phase of contact with the Taliban and its allies to explore a possible reconciliation deal. Nobody in the U.S. military is better at the mix of fighting and talking in such ambiguous situations.