Military operations against terrorism are essential in places like Iraq and Afghanistan, but Islamic extremism will be defeated as much - if not more - in the Muslim heart and mind as on the battlefield.

So, at least, suggests a new Pakistani survey.

The Pakistan branch of ACNielsen did the poll for the D.C.-based nonprofit Terror Free Tomorrow. The key finding: Pakistan - long a hotbed of terrorism and extremism, and still the suspected hiding place for Osama bin Laden, and other senior terrorist leaders - now holds the United States in higher regard than at any time since 9/11.

More: Support among Pakistanis for al Qaeda and terrorism has plummeted to its lowest level in over four years.

What's behind this seismic shift in Pakistani public mood?

Seeing Afghanistan gaining ground may help, but the pollsters point to U.S. humanitarian aid and assistance in the aftermath of October's devastating earthquake in Pakistan.

The quake (7.6 magnitude) killed over 75,000 people, injured tens of thousands and left 3 million homeless. In the tragedy's aftermath, the United States, quickly pledged nearly $500 million for relief/reconstruction efforts, including $300 million in humanitarian aid, $100 million to support Pentagon relief operations - plus over $70 million in private American donations.

And we delivered on those promises, starting right away.

Over 250 U.S. military and civilian cargo airlifts delivered more than 7,000 tons of medical supplies, food, shelter material, blankets and rescue equipment to Pakistan. And more than 1,000 American civilians traveled to South Asia to lend a hand.

U.S. military helicopters have flown over 3,000 missions delivering more than 10 million pounds of relief supplies and moving more than 15,000 people, including over 4,300 Pakistanis desperately in need of medical attention.

A 125-person Navy "Sea Bee" construction unit is clearing debris, erecting support facilities and building refugee camps to ward off the harsh local winter; a U.S. Army "MASH" medical unit has provided urgent medical care to over 9,000 injured people.

Cut to the poll of 1,450 Pakistanis, surveyed last month:

* Because of America's response, 78 percent of those asked have a more favorable opinion of the United States, with the strongest support coming from Pakistanis under 35.

* Positive opinions of the United States in Pakistan doubled from 23 percent in May to more than 46 percent in November; negative views fell from 48 percent to 28 percent.

* Over the same period, support for the "mythical" Osama bin Laden dropped from 51 to 33 percent; those opposing the al Qaeda boss jumped from 23 percent to 41 percent.

* Those who see terrorist suicide attacks as never justifiable shot up from 45 percent to 73 percent.

* Biggest bombshell of all: The United States proved more popular than both other Western countries and radical Islamist groups.

Not all the news was good: Pakistanis increasingly oppose the U.S.-led War on Terror - up from 52 percent in May to 64 percent now.

OK, so what does this mean?

First, America humanitarian aid and assistance plainly can make a difference in Muslim-world attitudes about the United States, terrorism and radicalism. (Polls have found a similar story in Indonesia - a nation that's been struck by al Qaeda-affiliate Jemaah Islamiya four times in three years - in the wake of the strong U.S. response to last December's tsunami.)

Second, the military element of the War on Terror remains unpopular in the Muslim world.

This last point can't rule out necessary actions - after all, America's failure to answer provocations plainly helped lead to 9/11: Al Qaeda not only grew confident that the United States would retreat whenever attacked, it used its growing series of successes against the United States as a powerful recruiting tool.

That said, it's plainly a mistake to overemphasize the use of U.S. "hard power" when "soft power" can also fight terrorism/radicalism, and support the development of political, economic and social freedom.

Third - and perhaps most important - we must recognize that support for al Qaeda and Islamic extremism has proven to not be absolute, but rather circumstantial and weakening. If it can be undermined in a crucible of Islamic radicalism/extremism like Pakistan, it can be overcome anywhere.

So, with a brand-spanking new parliament in Afghanistan, a third successful round of nationwide voting in Iraq - and good news like this from Pakistan - it's no wonder the world hasn't heard a peep from Osama bin Laden in almost a year.

Peter Brookes is a Heritage Foundation senior fellow. His book, "A Devil's Triangle: Terrorism, WMD and Rogue States," is just out.