In Iraq, where al-Qaeda operatives thrived after the 2003 U.S. invasion, Sageman says, public sentiment turned against the group two years ago, as Muslim civilian deaths mounted from repeated al-Qaeda attacks.
"Al-Qaeda simply overreached," Sageman says. "When they started killing heads of tribes, the tribes turned against them. … Al-Qaeda is dying."
Mueller acknowledges bin Laden's group has lost key commanders, but says its new leaders have "the ability to breathe new life into the organization."
In a telephone interview, Mueller says these new leaders are tapping recruits with planning or technical expertise to fill empty slots. To counter that, Mueller has tried to transform the bureau — part of larger, post-9/11 reorganization of federal law enforcement and intelligence agencies — to emphasize the prevention of new attacks, rather than to focus solely on prosecutions. Among the changes in the bureau since 9/11:
• The number of FBI agents assigned to counterterrorism or intelligence duties has more than doubled, from 2,514 to 5,419;
• The number of Joint Terrorism Task Forces has tripled, to 106 from 35, while the members of those task forces from federal, state and local agencies have soared, to 4,421 from 912;
• The number of intelligence analysts has more than doubled, to 2,511 from 1,023.
Mueller says the realignment of resources, the creation of the Department of Homeland Security and a greater emphasis on intelligence have helped avert attacks since 2001.
"We can no longer count on the oceans to protect us," he says.
On the crowded streets of Sana, Yemen, there is evidence that al-Qaeda is very much alive.
The attack last September on the U.S. Embassy in the Yemen capital underscored the growing concern among U.S. national security officials.
Yemen is fighting an escalating Shiite rebellion along its northern border, a secessionist movement in the south, rampant poverty and a shrinking water supply — all favorable conditions for al-Qaeda and its allies to recruit and train operatives, analysts say.
"Everything that allowed Saudi Arabia to largely defeat al-Qaeda — the big central government, wealth, religious message — doesn't exist in Yemen," says Christopher Boucek, a Middle East analyst with the Carnegie Endowment for International Peace. "It's a dangerous situation."
The country of 24 million people is the ancestral homeland of Osama bin Laden. Yemen's coastal city of Aden also was the scene of one of al-Qaeda's deadliest attacks against the United States: the 2000 bombing of the USS Cole, which killed 17 sailors.
A measure of U.S. concern has come in the past two months, as delegations of U.S. officials, including Gen. David Petraeus, the top U.S. commander in the Middle East, and Sen. John McCain, the Arizona Republican and former presidential candidate, have traveled to the Yemen capital to discuss the country's counterterrorism strategy.
Al-Qaeda's presence in Yemen also is at the center of a debate over what to do with 94 Yemeni prisoners set to be released from the Guantanamo Bay, Cuba, detention center when it closes in January 2010.
Yemen's government has said it expects the detainees to be returned home.
"The (Yemen) government acknowledges the challenges it faces," Yemen Embassy spokesman Mohammed Al-Basha says. "We have been open and transparent with our allies with regards to these challenges and continue to ask … for development and security assistance."
U.S. officials fear that allowing the prisoners to return home would add to the terrorist ranks.
"The government of Yemen has its hands full," says Sen. Lindsey Graham, R-S.C., who traveled with McCain and other senators to Sana last month. "It would be a poor policy decision to send these (detainees) back."
On Sept. 11, Mueller will be in his office, as he was when his mission changed the instant suicide hijackers hit their targets at the World Trade Center and the Pentagon and slammed into the Pennsylvania countryside.
"Sept. 11 will be another day that we make certain that it doesn't happen again," he says.
He worries that people have become "complacent" in the absence of additional attacks.
"We should lead our lives," the director says. "(But) there should be a depth of appreciation for what happened."