WASHINGTON -- Israel's war with Hezbollah is a war to secure its northern border, to defeat a terrorist militia bent on Israel's destruction, to restore Israeli deterrence in the age of the missile. But even more is at stake. Israel's leaders do not seem to understand how ruinous a military failure in Lebanon would be to its relationship with America, Israel's most vital lifeline.

For decades there has been a debate in the U.S. over Israel's strategic value. At critical moments in the past, Israel has indeed shown its value. In 1970, Israeli military moves against Syria saved King Hussein and the moderate pro-American Hashemite monarchy of Jordan. In 1982, American-made Israeli fighters engaged the Syrian air force, shooting down 86 MiGs without a single loss, revealing a shocking Soviet technological backwardness that dealt a major blow to Soviet prestige abroad and self-confidence among its elites at home (including Politburo member Mikhail Gorbachev).

But that was decades ago. The question, as always, is: What have you done for me lately? There is fierce debate now in the U.S. about whether in the post-9/11 world Israel is a net asset or liability. Hezbollah's unprovoked attack on July 12 provided Israel the extraordinary opportunity to demonstrate its utility by making a major contribution to America's war on terror.

America's green light for Israel to defend itself is seen as a favor to Israel. But that is a tendentious, misleadingly partial analysis. The green light -- indeed, the encouragement -- is also an act of clear self-interest. America wants, America needs, a decisive Hezbollah defeat.

Unlike many of the other terror groups in the Middle East, Hezbollah is a serious enemy of the United States. In 1983, it massacred 241 American servicemen. Except for al-Qaeda, it has killed more Americans than any other terror organization.

More importantly, it is today the leading edge of an aggressive, nuclear-hungry Iran. Hezbollah is a wholly owned Iranian subsidiary. Its mission is to extend the Islamic Revolution's influence into Lebanon and Palestine, destabilize any Arab-Israeli peace, and advance an Islamist Shiite ascendancy, led and controlled by Iran, throughout the Levant.

America finds itself at war with radical Islam, a two-churched monster: Sunni al-Qaeda is now being challenged by Shiite Iran for primacy in its epic confrontation with the infidel West. With al-Qaeda in decline, Iran is on the march. It is intervening through proxies throughout the Arab world -- Hezbollah in Lebanon, Hamas in Palestine, Moqtada al-Sadr's Mahdi Army in Iraq -- to subvert modernizing, Western-oriented Arab governments and bring these territories under Iranian hegemony. Its nuclear ambitions would secure these advances, give it an overwhelming preponderance of power over the Arabs and an absolute deterrent against serious counteractions by the United States, Israel or any other rival.

The moderate pro-Western Arabs understand this very clearly. Which is why Egypt, Saudi Arabia and Jordan immediately came out against Hezbollah and privately urged the U.S. to let Israel take down Hezbollah. They know that Hezbollah is fighting Iran's proxy war not only against Israel but against them and, more generally, against the United States and the West.

Hence Israel's rare opportunity to demonstrate what it can do for its great American patron. Defeating Hezbollah would be a huge loss for Iran, both psychologically and strategically. It would lose its foothold in Lebanon. It would lose its major means to destabilize and inject itself into the heart of the Middle East. It would be shown to have vastly overreached in trying to establish itself as the regional superpower.

The U.S. has gone far out on a limb to allow Israel to win and for all this to happen. It has counted on Israel's ability to do the job. It has been disappointed. Prime Minister Ehud Olmert has provided unsteady and uncertain leadership. Foolishly relying on air power alone, he denied his generals the ground offensive they wanted, only to reverse himself later. He has allowed his war Cabinet meetings to become fully public through the kind of leaks no serious wartime leadership would ever countenance. Divisive Cabinet debates are broadcast to the world as was Olmert's own complaint that ``I'm tired. I didn't sleep at all last night." (Haaretz, July 28.) Hardly the stuff to instill Churchillian confidence.

His search for victory on the cheap has jeopardized not just the Lebanon operation, but America's confidence in Israel as well. That confidence -- and the relationship it reinforces -- is as important to Israel's survival as its own army. The tremulous Olmert seems not to have a clue.