The debate over Afghan strategy — the Af in our AfPak policy — has overshadowed an equally daunting challenge: Can we figure out how to improve relations with Pakistan?

In many ways, Pakistan is the more important of the AfPak duo. Al-Qaida leaders and Afghan Taliban maintain havens in Pakistan. Pakistani militants dream of seizing their country’s nuclear weapons.

Pakistan’s civilian government and army finally struck back against the Taliban in April, after the militants threatened the capital; the Pakistani public and press backed this offensive. But public opinion is negative about any cooperation with the United States against the jihadis; the mistrust of our country is profound.

Only 16 percent of Pakistanis expressed a favorable view of the United States in a recent Pew Research Center survey. Only 13 percent had confidence in President Obama — a mere bump of 6 percentage points over former President George W. Bush.

And, critically, 76 percent are opposed to Pakistan’s partnering with the United States in drone attacks against al-Qaida and other extremists — even though those drones killed the man accused of murdering former Prime Minister Benazir Bhutto.

Those negative numbers reinforce the army’s reluctance to tackle the Taliban along the Afghan border. They make it more difficult for Pakistani President Asif Ali Zardari to continue working with the Americans.

Reversing these negative attitudes is essential to strengthen cooperation against the militants. But can it be done?

One promising step is congressional passage last week of a bill that triples U.S. civilian aid to Pakistan — to $1.5 billion a year for the next five years. In the past, says the Pakistani ambassador to Washington, Husain Haqqani, his countrymen considered America a fickle friend who deserted Pakistanis when it didn’t need their military cooperation. “So the long-term aid commitment is positive,” Haqqani said.

So is the fact that, unlike in the past, this multiyear aid package is for schools, roads, agricultural development, and water management, not arms. The legislation also calls for more oversight of aid delivery than in the past, in hopes that these projects will actually get built.

A skeptic could be forgiven, however, for noting that Washington has won few plaudits for previous civilian aid efforts in Pakistan, including a recent $300 million in humanitarian relief for refugees fleeing the Taliban.

Which brings us to the heart of the matter: Most Pakistanis are unaware of U.S. help. They are more likely to believe an endless series of anti-American rumors. Example: The recent baseless claim that 1,000 Marines were about to storm Islamabad — no doubt to seize Pakistani nukes.

One Pakistani journalist told the New York Times: “Most Pakistanis are exposed to the popular media and to extremist clerics, who provide this perception. The American side of the story is not available to the people.”

Unless the United States develops a strategy for reaching Pakistanis, with real stories of U.S. aid — not fake “public diplomacy” — the local population will continue to view us with hostility, no matter how much aid money we send there. That hostility translates into gains for al-Qaida and the Taliban.

Richard Holbrooke, Obama’s special representative for Afghanistan and Pakistan, is well-aware of this problem. Yet, despite lots of talk, no solid U.S. media strategy for Pakistan has gotten off the ground.

When I ask Pakistani colleagues what U.S. officials should do, they quickly provide a list:

1. Pay attention to Pakistani media. Have U.S. officials constantly appear on Pakistani TV, even hostile channels such as GEO (Holbrooke did it) and challenge every media lie. Be more proactive. Example: Ambassador Anne Patterson invited Pakistani media to tour the embassy grounds and see that there are only eight Marines on the premises.

2. Put a team of U.S. media specialists on the ground in Pakistan, who know the language and the culture and can devise new ways to communicate with Pakistanis — whether by FM radio, or Internet, or interviews. “Recreate a USIA for Pakistan,” one Pakistani journalist told me, a reference to the wretched decision in the 1990s to disband the U.S. Information Agency.

3. Publicize the good work the United States does inside Pakistan. (We know this can work; remember the plaudits America got for 2005 earthquake relief in Pakistani Kashmir, aid that was publicized.) Obama should sign the Kerry-Lugar bill at a ceremony with all the Pakistani correspondents in Washington invited to attend.

4. Above all, listen to the 16 percent of Pakistanis who want good relations with the United States, and to Pakistani-Americans.

Our Pakistani friends can provide valuable advice on how to punch through the conspiracy theories and get Pakistanis to hear what we’re saying. And we need to figure out how to do this — very soon.