Pakistan is a mess, it’s making a worse mess of Afghanistan, and there is not much the United States can do directly to clean it up. This is the unfortunate state of affairs that cast a shadow over President Obama’s meeting with the presidents of Pakistan and Afghanistan on Wednesday.

The pressing problem is that the Taliban and others who espouse al-Qaeda’s civilizational ideals control large and expanding parts of northwestern Pakistan. The turmoil is spreading across Pakistan’s border with Afghanistan, where the Taliban has in recent years regrouped and posed a growing threat to the Afghan government and NATO forces.

The Pakistani president, Asif Ali Zardari, is a weak leader whose venality guides his sympathies westward. He nonetheless has been too accommodating of the Taliban during his short time in power, hoping until recently that they would more or less behave themselves in exchange for a greater degree of autonomy. That policy was an extension of the false hope of Pervez Musharraf, his predecessor, who struck a peace deal with the Taliban but did not take decisive action against it when it violated the deal.

Zardari’s government seems weaker by the day. Last week brought reports that the Obama administration was reaching out to his main rival, the former Pakistani prime minister Nawaz Sharif, whose ties to the Islamists make him a dubious figure, possibly a dangerous one.

While the probability of a Taliban regime’s taking power in Islamabad is not yet high, the amount of area under Islamist control increases. Al-Qaeda and its affiliates have tried—with an unknown degree of success—to infiltrate the military and bureaucratic institutions that control Pakistan’s nuclear arsenal. The confluence of state terrorist sympathizers, non-state terrorist actors, and nuclear weapons is no less than horrifying, and points to the need for a Pakistani government willing to confront and defeat the jihad in its midst.

The Taliban has always been at root a Pakistani phenomenon; the Afghan Taliban regime that the United States toppled following 9/11 had been propped up by elements of the Pakistani army and intelligence services. Those same elements now suspect that the U.S. commitment to Afghanistan is tenuous, and fear Indian influence in Afghan affairs. They continue to support Taliban proxies inside Afghanistan in anticipation of a power vacuum.

For all its diplomatic dancing around the Zardari–Sharif rivalry, the U.S. has precious little control over Pakistani politics. Any obvious U.S. influence is decidedly unpopular, and the Pakistani government—even those elements of it that are sympathetic to the U.S.—is accordingly wary of direct American initiatives. The deployment of regular combat troops would be unthinkable; strikes from U.S. Predator drones have provoked outcries.

Yet the Taliban are far from popular, and the brutality with which they have exercised their expanded dominion has deepened their unpopularity. Zardari appears to have moved away from his policy of conciliation and toward one of military action, although the action so far has combined inefficacy with indiscriminate destruction. It is not in question that a Pakistani government could rout the Taliban if it were (1) sufficiently stable and (2) earnestly resolved. What hinders both (1) and (2) is the divided soul of the country’s security and military establishment, over which Zardari and the civilian leadership exercise a highly limited degree of power.

The goal of U.S. policy should be to change this establishment’s perception of its interest. And the best way to do that is with a continued display of power and resolve in Afghanistan. This would make it clear that the United States is and will continue to be the guarantor of the regional security order, and that Pakistan must calculate accordingly.

The United States should not downplay its ties to India for fear of offending Pakistan, but to the contrary should strengthen them at every opportunity. This too will influence the strategic calculus: To the extent that Pakistan’s security and military establishment sees the futility of fighting a symbolic proxy war over Kashmir, it will be less likely to view jihadists as an asset.

U.S. economic and military aid to Pakistan should continue but should be more explicitly conditioned on anti-Taliban measures. Such measures should be rewarded both quickly and liberally. Likewise, channeling some of that aid to improving Pakistan’s local police and law enforcement would provide an important avenue of advancement against the Taliban, which thrives in the atmosphere of corruption.

The people of Pakistan do not, on the whole, care for Islamism; Pakistani civil society is well developed; Pakistani economic interests lie in political openness and trade, via Afghanistan, with Central Asia. It is not outlandish to hope that these currents, over time, will wash the Taliban into a much-deserved oblivion. Until then, we can do little more than show our strength and reward those who trust in it.