Pakistan is often described as the most urgent foreign-policy headache facing President-elect Barack Obama.

Al-Qaida and the Taliban have sunk roots in its tribal regions, from which they mount attacks on coalition troops in Afghanistan. A frustrated Bush team has unleashed missile attacks on militants in Pakistan, but the country’s government warns that the strikes undercut its own efforts to fight the jihadis. Meantime, the militants destabilize a country with nukes.

But wait. There’s some good news. Despite the rhetoric about missiles, there are good prospects for stronger U.S.-Pakistan cooperation if Obama moves astutely and fast.

Pakistani officials say there has been substantial improvement in relations between U.S. and Pakistani intelligence officials. The new head of Pakistan’s ISI intelligence agency, Lt. Gen. Ahmed Shuja Pasha, visited Washington in late October for talks with our top intelligence chiefs, and the meetings went very well.

“Everyone in Washington knows there is no lack of will on the part of Pakistan’s elected leadership to combat terrorism,” Pakistan’s ambassador to Washington, Husain Haqqani, told me. “We are working together to assure capacity.”

Such cooperation is key, since America has little human-intelligence capacity in the region where the militants are hiding. Relations between the CIA and ISI had been at a nadir, but they are being rebuilt. Pakistanis say they are cleaning out ISI elements that have been too close to militants. Cooperation is also developing among the Pakistani military, Afghan forces, and NATO forces in Afghanistan.

The results are already apparent in the more successful targeting of Predator missiles. Gen. David Petraeus said last week that recent attacks killed three top extremist leaders. Pakistani officials say an Oct. 16 strike in South Waziristan got Khalid Habib, who ranked fourth in the al-Qaida hierarchy and recruited operatives for future attacks on the United States.

The bottom line: Despite their public critique of Predator air strikes, Pakistani officials are providing intelligence that helps U.S. missiles find their targets and limit collateral damage. Nevertheless, such strikes infringe on Pakistan’s sovereignty and carry big political risks.

Pakistan’s elected leaders are caught in a bind. President Asif Ali Zardari recognizes the threat the militants pose to Pakistan’s stability. And the Pakistani military is making new efforts to fight jihadis in tribal regions. But the Pakistani public is strongly opposed to the strikes.

Most ordinary Pakistanis still believe the fight against militants in their country has been imposed on them by the United States. “Every one of these attacks puts relations (with America) under strain,” said Brookings Institution South Asia expert Bruce Riedel. If Pakistanis perceive Zardari as too close to the Americans, his government will be in peril; waiting in the wings is opposition leader Nawaz Sharif, who is far less sympathetic to America’s concerns.

This means that a President Obama will have to be extremely judicious in conducting any strikes into Pakistan. As the Bush administration learned, sending ground forces into Pakistan is hugely counterproductive. A cross-border U.S. special forces operation on Sept. 3 caused an uproar.

An irate Ehsan ul-Haq, who has headed the ISI and the joint chiefs of Pakistan’s army, told me the strike undermined the government’s efforts to win the Pakistani public’s support for fighting the militants. “We had just started to advertise (to Pakistanis) that this is your war,” he said. “And all of a sudden there was a U.S. attack.” He urged the United States, “Work in a way that doesn’t embarrass the government in Islamabad.”

As for missile strikes, they would be more effective as part of a broader effort at expanding U.S.-Pakistan cooperation.

Obama has said the United States should strike if it has actionable intelligence against Osama bin Laden. “They don’t have the intelligence,” said Haqqani, “but the moment they do, we’ll go after him.”

I would add that, ideally, it would be a cooperative effort.

Better cooperation also means aiding Pakistan’s elected government, which is politically weak and economically desperate.

First, the United States should assist Pakistan in getting International Monetary Fund help to emerge from its severe economic crisis. And the Obama administration should push ahead with Sen. Joseph Biden’s plan to triple nonmilitary aid to Pakistan to $1.5 billion annually for 10 years. This would amount to about one month of U.S. expenditures in Iraq, yet it could help convince Pakistan’s public that we are an ally.

Finally, Obama could build a more cooperative relationship with Pakistan’s military, providing technology and equipment for the fight against jihadis. This has proved difficult in the past. But Pakistan’s serious plight gives Obama new opportunities, including a chance for quiet diplomacy between Pakistan and India on Kashmir.

“There is an opportunity for the United States to say Pakistan is a strategic partner,” said ul-Haq. “You’ve adopted India. What about Pakistan? What is the message to the people of Pakistan?”

Obama has a chance to craft a new message that will be crucial to Pakistan and us.