What matters at least as much as the killing of al-Qaida top terrorist Abu Musab al-Zarqawi in Iraq is that we, in America, appreciate it for the important battlefield victory it truly is.

Dubbed "the prince of al-Qaida" by Osama bin Laden, al-Zarqawi was the apparently invincible face of a campaign of hideous carnage in Iraq — a barrage of kidnappings, shootings, bombings, assassinations and beheadings. He had carried this bloodshed over into his native Jordan and threatened to expand well beyond.

Part of the battle against such enemies is simply to reduce them in the public imagination to mortal scale. It was a smart move when the U.S. military a few weeks ago released video footage ridiculing al-Zarqawi as a pudgy thug who did not know how to handle a gun. It is a much greater leap that, thanks to a combination of Iraqi intelligence and U.S. military forces, he has now been killed, along with seven of his aides, in an air strike Wednesday on a house where they were hiding north of Baghdad.

On four levels, al-Zarqawi's death has global ramifications.

The first and most basic stems from the command position he enjoyed. While the leaders of al-Qaida like to dispatch suicide bombers, they themselves are not inclined to suicide. Their larger strategy in launching terrorist attacks on everything from police stations to mosques to wedding parties is to destroy the bonds of trust on which decent societies depend, erode the will to fight back, and clear the way for a takeover of power. Bin Laden and his deputy, Ayman al-Zawahiri, issue bloodthirsty messages from their hideaways, but they have not offered themselves up for the kind of sacrifices they require of their followers. It is the capture or killing of such terrorist kingpins — and al-Zarqawi was one — that serves as the real disruption and deterrent.

Second, al-Zarqawi was found with the help of Iraqis, some of whom have been dancing in the streets to celebrate his death. In Iraq, that is a sign not only of opposition to terrorists but of the courage to stand up and defy them. It is of a piece with the decisions of millions of Iraqis over the last two years to turn out, despite death threats, to vote. They are telling each other, and the world, that they are willing to take large risks to build a decent, free society.

Third, in raids that accompanied the strike on al-Zarqawi, U.S. and Iraqi forces have acquired what White House spokesman Tony Snow has described as a "treasure trove" of intelligence. The cars, explosives, guns, ammunition and safe houses required for al-Qaida's murderous operations turn up courtesy of a network that points to other nodes. That may not immediately stop other operations already in place, but it can have a big effect down the road, leading to other top figures in the command.

Finally, this is an excellent moment to step back and look at just how far in this war we have come. Five years ago, al-Qaida's commanders, from their safe haven in Afghanistan, were training thousands of terrorists and planning the Sept. 11 strike on a sleeping America. In Iraq, Saddam Hussein ruled by terror, with a record of exporting brutality and war from Baghdad at any opportunity to wherever he could reach — invading his neighbors, rewarding Palestinian suicide bombers, and openly rejoicing over Sept. 11.

Today, elected governments lead Afghanistan and Iraq, which has just completed its cabinet lineup. Bin Laden is afraid to venture out of hiding; Saddam, pulled from his spider hole, is on trial in Baghdad. And now, al-Zarqawi is dead, and the circumstances of his death may encourage decent people not only in Iraq but elsewhere to help hunt down his collaborators.

The greatest weakness of the United States in this war has been our tendency, within our own domestic debate, to quickly dismiss our victories and dwell on each al-Qaida bombing or beheading as a sign of impending defeat. The death of al-Zarqawi needs to be understood as a sign that the deeper currents are running our way.

Claudia Rosett is a journalist-in-residence with the Foundation for the Defense of Democracies. Reach her at claudiarosett@hotmail.com. She wrote this commentary for the Philadelphia Inquirer.