Certainly the Gulf region is of high importance but let's make a distinction between Iraq and the entire Gulf. How far will controlling Iraq get you?
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In a dream ending for the chapter of history being written now in Iraq, neo-conservatives fantasised before the war about a privatised, pro-American Iraqi oil industry. This would have access to the world's second largest hydrocarbon reserves and produce so much oil that Saudi Arabia, in charge of Opec, would lose its grip on petrol prices.
The world would then be swimming in inexpensive petrol - the cost of which would be dictated by the market, not by an anti-American price-fixing club run by Riyadh. Low prices would also mean falling revenues for oil-producers, which in the Middle East might precipitate the collapse of regimes hostile to the US. These hopes are now being dissipated like sand before the desert wind.
Oil is dribbling, rather than pumping, from Iraq's bomb-blasted oil industry. Sabotage and theft mean Iraq's oil production remains at a fraction of the levels achieved under Saddam. With reconstruction failing to take off, there is little sign of a post-Ba'athist dividend in the form of low oil prices. The result is that US action in Iraq has not weakened Opec, and hence Saudi Arabia, but strengthened it
Bush's oil move backfiresNot looking like it's so far just now.

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The US has decided to leave the running of Iraq's oil industry to Iraqis after failing to put together an international oil advisory board. The move is likely to boost non-US oil companies' chances of winning lucrative investment contracts in the country.
Companies such as BP, Royal/Dutch Shell and Total have worried that US companies would be given preferential treatment in Iraq and some analysts have warned that companies from countries that had opposed the war against Saddam Hussein could be frozen out of making investments in Iraq. "In a way it's reality catching up with them [the US]," said one executive...
Oil to Come Under Iraqi Control as US Fails to Form Advisory BoardNor does it seems as though the administration really wants its that much.