There is no easy victory in sight in Afghanistan, but we are closer to accomplishing our goals than many assume. By late 2014 it will no longer be necessary to keep significant numbers of combat troops there.

The recent accord transferring main night-raid responsibility to Afghan forces, while perhaps a bit hurried at Afghan insistence, nonetheless reflects progress and is welcome news. At a time when discussion of the war has become very negative in the U.S., we need to bear these points in mind—and resist self-fulfilling fatalism and a premature withdrawal.

The good news is that the Obama administration appears unlikely to waver anytime soon. Its officials have declared that no further draw downs will be considered until the current one, bringing U.S. troops down to 68,000 from 100,000 by the end of September, is complete. In particular, we need to see how conditions evolve in the east, where this year’s main anti-insurgency efforts will likely occur. However, the more worrisome news is that in a political year, with electoral pressures rising, a steady policy hand in the White House should not be assumed indefinitely into the future.

Overall, while NATO and the Afghan government have plenty of problems, the Taliban have been losing the war on the battlefield and remain hugely unpopular among the Afghan population. Our problems pale next to the enemy’s. It can still win by exploiting our vulnerabilities, but only if we let it.

The Taliban narrative goes something like this: President Hamid Karzai’s government is a corrupt puppet that will fall once NATO troops depart. NATO nations are irresolute infidels, looking for any excuse to leave a war they know they can’t win. The massacre of 17 Afghans by U.S. Sgt. Robert Bales last month is more proof that Westerners don’t care about the Afghan people. All security trends favor the Taliban, as spectacular attacks—like the assault last September on the U.S. Embassy—from Kabul to Kandahar to Kunduz reveal over the last two years.

Every point in this account is something between a huge exaggeration and a cynical lie:

In fact, Kabul is a fairly safe city—and it’s safe largely because Afghan forces protect it. Less than 1% of all enemy-initiated attacks occur there; statistically it is far less dangerous than Iraq’s Baghdad or Pakistan’s Karachi. Yet the narrative reinforced by Taliban media releases emphasizes the spectacular attacks. There hasn’t been one in months, but the daily news cycle tends not to note such favorable trends.

Violence in the south is down by a third to half, despite the Bales tragedy and a recent “green on blue” incident in which an Afghan killed two British soldiers. Many if not most Taliban weapons caches are gone, NATO officials say, and governance has improved substantially in Helmand and Kandahar provinces. The north and west are worse than they were in 2002-07 but somewhat better than in 2009-10. The situation in these regions is no longer deteriorating.

Afghan security forces are leading 40% of operations nationwide. According to the commander of U.S. forces, Gen. John Allen, these soldiers are “better than we thought.” The Taliban are acutely aware that Afghan security forces are now 330,000-strong and much improved. That is why the Taliban are desperate to disrupt their partnership with NATO.

Mr. Karzai is still a challenge. We cannot afford a repeat of the 2009 undemocratic presidential election. Mr. Obama’s handling of that process was his biggest mistake in the war. But the huge news is that Mr. Karzai has firmed up his plans to step down in 2014. We now need to get on with supporting Afghan political parties, opposition candidates and parliament to create the ingredients for a good 2014 election to replace him.

The Taliban may talk with bravado, yet they have been decimated in many ways. Sanctuaries in Pakistan provided by that country’s Inter-Services Intelligence organization still protect Taliban leaders. But we have been taking hundreds of local Taliban commanders off the battlefield per year, with the result that the average age of those who remain has declined to 23 or so, from 35. In short, we are hurting, but the enemy is hurting more. Their actions demonstrate it. For instance, While it is regrettable that the Taliban have suspended peace talks, their mere interest in such talks is unprecedented. It probably reflects their own, and Pakistan’s, sense of their vulnerabilities.

Afghanistan still has huge problems, and no clear victory is within reach by 2014. We lost that opportunity years ago, and the insurgency is likely to persist. But the goal can and should be that Afghan forces will increasingly contain and combat it on their own. At that point, perhaps 10,000 to 20,000 foreign forces can suffice—to mentor Afghan units in the field, and for air power and intelligence support, training and special operations.

Moving to such a small force prematurely, however, would leave the country’s east too infiltrated by insurgents. It would also prevent the partnering and apprenticeship work with Afghan units in the field—which requires NATO combat formations, not just advisers. Things are better than many realize. We have an exit strategy that is already being implemented. So it is important not to rush it.