Around the world, terror groups are finding many former havens no longer particularly safe nor welcoming.
The reason: National leaders can all see what happened in Afghanistan, and none wants anything like that to happen to them.
Thus nations whose wilder regions have long harbored terror camps, such as Yemen and Sudan, are at least attempting something of a crackdown. Countries that have long battled insurgencies with terrorist links - the Philippines, for one - are eager to redouble their efforts, with increased US help.
The next stage of the American-led war on terrorism will likely focus on efforts to help along this door-shutting trend, as opposed to launching a major military action against a hard target such as Iraq. Some of these actions will be visible, say US officials. Many others will not be.
"We're encouraged by the range of counterterrorism cooperation and actions that are taking place throughout the world," said State Department spokesman Richard Boucher on Jan. 7.
The Al Qaeda terrorist network operates in 60 to 70 countries, according to Gen. Tommy Franks, commander of the US military effort in Afghanistan.
Worldwide, international law-enforcement efforts have resulted in the arrests of a reported 800 to 1,000 suspected Al Qaeda operatives or sympathizers.
Many of these detainees were rounded up in Western Europe, where governments have both the means and the will to lead their internal crackdowns. But some were arrested in nations that have long been home to terrorist camps, either due to tolerance on the part of local governments or the inability of national leaders to fully control their territory.
Take Yemen. Following a visit to Washington late last year by President Ali Abdullah Saleh, Yemeni officials appear to have begun a real effort to root out suspected Al Qaeda operatives who have long lived in remote regions bordering Saudi Arabia.
In December, Yemeni troops trained and equipped by US forces attacked a tribal group thought to be harboring three key Al Qaeda operatives. At least 24 soldiers and four tribesmen were killed in the battle, according to Yemeni officials.
Yemen has announced plans to deport on immigration charges 80 students and teachers from a fundamentalist Islamic institute. But the three terrorist leaders who were the target of the December attack remain at large.
"Security forces know where they are hiding but are ... working to specify the exact location before we take any steps," Yemeni Foreign Minister Abubakr al-Qibi said on Jan. 6.
Sudan has made a similar surprising turnabout. Osama bin Laden lived in Sudan between 1991 and 1996, and openly ran his business and terror operations from an office building in Khartoum. Testimony by an Al Qaeda turncoat in a federal trial in New York even described an attempt by Mr. bin Laden to buy fissile material through a criminal organization that had links to Sudan's Islamic government.
But today Sudan is cooperating with US antiterrorism efforts, say American officials. Khartoum has provided extensive intelligence about bin Laden's stay in the country. Officials have arrested a number of suspected Al Qaeda operatives and made them available for US interrogation.
Another longtime terrorist haven, Somalia, represents a more mixed case.
Somalia remains a largely lawless nation riven by faction and controlled by warlords. US officials consider it perhaps the most likely nation in the world to become the next Afghanistan - that is, a country virtually hijacked by a terrorist group for its own purposes and activities.
Since Al Qaeda fractured and ran in Afghanistan, the US military has increased its aerial surveillance by Navy P-3 spy aircraft along the Somali coast. It has begun checking some boats in the Arabian Sea to ensure that the remnants of Al Qaeda's organization have not fled through Pakistan or Iran to a possible escape by sea.
At the same time, US diplomats have been in touch with the transitional government of President Abdiqassim Sala Hassan, who has said he will support US efforts to root out any terrorist presence in Somalia.
The US does not recognize Mr. Hassan's government and is convinced that people linked with terrorism remain in Somalia, according to a US official knowledgeable about the region. But neither does Washington think that bombs would make any difference in this situation. There are no major training camps or other military targets remaining in the area.
After Afghanistan, Somalia is an obvious next step, says the official. "Eventually we will get to Somalia, whether now or in six months' time," says this source.
One problem in these countries is that it can be hard to determine whole-hearted cooperation from something that represents simply going through the motions.
Nor are national leaders doing this for free. They want support, tacit if not overt, and money. "I sort of wonder, what is the price of all this?" says Radha Kumar, senior fellow in peace and conflict studies at the Council on Foreign Relations. This is true even for enthusiastic countries such as the Philippines. President Bush has promised to increase its military aid to $100 million a year, from the current $2 million.
Staff writer Danna Harman in Nairobi contributed to the report.