The current fighting between rival Shiite militias in Basra, the strategically crucial Iraqi port at the head of the Persian Gulf, is simultaneously of vital importance and exceptionally confusing to outsiders unfamiliar with the fractured chaos that Iraq has become. But it still should teach sobering, as yet unlearned policy lessons to U.S. leaders.

The fighting first of all underscores the myth spread by the George W. Bush administration and neoconservative commentators over the past five years that Saddam Hussein, al-Qaida and a few hundred Sunni Muslim extremists were at the source of all Iraq's problems. It also demonstrates the hollowness of the short-term tactical successes achieved by U.S. Gen. David Petraeus in his "surge" strategy over the past 15 months.

For the fighting in Basra has nothing to do with the continuing Sunni-Shiite civil war in central Iraq and Baghdad. The surge strategy could not prevent it from breaking out for the very good reason that even with that strategy, the United States has no troops to spare to create any kind of security at all across all of Shiite-inhabited southern Iraq.

The fighting also nails the old, resilient, imperialist myth that the British "know" Iraq and the Arab world and can operate as skilled, successful masters in it. That myth was certainly not true during the 40 years from 1918 to 1958 when the British either dominated the region or remained a significant presence in it, and it is certainly not true today. The remaining British troops at Basra remain holed up in their last stronghold at the city's international airport from which they can be rapidly airlifted out.

Finally, the fighting shoots down yet another myth, that Petraeus, his "surge" strategy and a supposedly "tough" and "courageous" U.S. policy to remain in Iraq has brought, or is visibly bringing, peace to that long-suffering country.

The drive by leading Iraqi Shiite militias, especially the Badr Brigades and their allies in the Baghdad government of Prime Minister Nouri al-Maliki is clearly a power-play by the main alliance of Shiite forces, increasingly backed by Iran, to secure control of Basra. They want to squeeze out the volatile, popular, but politically inept Moqtada al-Sadr.

Sadr and his Mehdi Army appear far more popular among ordinary people in the Basra region than the array of forces opposing him from the Badr Brigades, al-Dawa and the Islamic Supreme Council of Iraq. But Sadr has been even more of a problem to the dominant Shiite constellation of interests than it has been to the United States.

U.S. policymakers appear to be welcoming the current move to force Sadr out of his Basra stronghold. But they should not cheer too soon. The anti-American Sadr is viewed with caution and considerable distrust by Iran too. And as Iranian President Mahmoud Ahmadinejad's recent successful visit to Baghdad showed, Tehran has built warm ties to the Maliki government, as well the leading Shiite militias, especially the Badr Brigades.

Far from securing Basra from Iran's allies, as Sadr is widely assumed to be, U.S. policymakers may soon find that the port, and their vital land supply routes to Baghdad, may soon be secured for Iraqi Shiite militia allies of Tehran instead.