(FORTUNE Magazine) – There was an important lesson, an OPEC home truth if you will, delivered at the meeting of the oil cartel in Vienna on April 24. Whether, and how much, OPEC would cut production in order to reverse the postwar plunge in crude prices really came down to this: How much were Saudi Arabia and its aggressive Oil Minister Ali al-Naimi going to cut production to keep prices stable? By implementing an OPEC cut of about a million barrels a day, Saudi Arabia proved it not only still runs the show, it is the show.

As the U.S. begins the process of rebuilding Iraq's oil industry, it's important to keep that lesson in mind, for the coming inevitable dance between Baghdad and Riyadh will have huge repercussions globally.

Much has been written about Iraq's real potential as a rival oil producer to Saudi Arabia. Baghdad, now Saddam-free and soon to be sanctions-free, has the second-largest proven reserve base in the world. Before the first Gulf war, Iraq produced up to 2.9 million barrels per day, and (after a lot of investment) some analysts believe production could be as much as five million barrels per day in three to five years. With some in the Bush administration (particularly in the Defense Department) pushing for a divorce from Saudi Arabia in the wake of Sept. 11, the idea that a Western-leaning Iraq could rival the House of Saud as a producer is critical to those who want to stick it to the Saudis. Big Iraqi production increases would, in theory, enable the U.S. to move military bases in the Middle East to Iraq, buy Baghdad's oil, and kiss the extremist-funding Wahhabi government in Riyadh goodbye.

That's the fantasy, anyway. Reality, alas, is different. What has always given the Saudis power in oil markets is their surplus capacity--how much extra production they can bring to the market at little extra cost. The Saudis have 1.9 million barrels per day of oil that they can tap with ease. That is far more than any other producer in the world (as of Sept. 2002 Iraq was second, at 1.2 million barrels per day of spare capacity, but it will be a while before the country's in any position to produce that much again). By taking production off the market or adding it, the Saudis have the ability, if not to set prices outright, at least to regulate them. And that they do--"very well, in fact," as oil consultant Philip K. Verleger says--for both political and economic purposes.

In the not too distant future Riyadh's political and economic focus will be squarely on Baghdad. In the short run the Saudis understand that for Iraq to be rebuilt and the country to have any hope for stability, Iraqi oil must come onstream, and the sooner the better. But beyond that the agenda in Saudi Arabia changes considerably. The sheikhs in Riyadh are not going to want the Iraqis getting too uppity. And in order to teach the new Iraqi oil powers a lesson, the Saudis could well boost production significantly and allow prices to come down sharply. That in turn would slow critically needed investment in Iraq's dilapidated oil sector.

This, of course, was not on the agenda at the OPEC meeting in Vienna, but psychology in oil markets will change significantly when Iraqi production is back at respectable levels in several months. The Saudis "won't let things get out of hand," says Verleger. "They have enough clout that they can decide to crank up production and encourage people to slow down." The Saudis, in other words, might strangle the baby before it gets too big. They've done it before (in the 1980s, for example, when Nigeria and other OPEC producers cheated on their production quotas, the Saudis flooded the market and drove prices down dramatically).

The fallout from this power struggle, which will continue well into the next U.S. presidential term, will be widespread. Russia and the other producers around the Caspian Sea will die a thousand deaths if the Saudis feel the need to flood the oil market to teach the Iraqis an early lesson. Governments in Russia and the other major former Soviet producers depend heavily on oil revenue. For them a steep oil-price decline would be disastrous. Though American energy consumers would get a short-term boost from significantly lower prices, the possible costs--including a devastated American oil patch and big economic trouble in Russia--might not be worth it. Oilmen famously like "stability" in prices, and the Saudis try to oblige. The key question in the post-Saddam oil world is, Will the new Iraq play along, or will the Saudis have to teach everyone, once again, who's boss?