(MONEY Magazine) – Javeed Mirza had a dream: snaring a piece of the $18.4 billion Iraq-reconstruction bill for his 25-employee software firm in Brooklyn.

He flew from J.F.K. to Jordan but quickly figured out that the real deals were being made in Baghdad. Mirza, 50, took a deep breath and called his wife back in the U.S., telling her he'd have to take the long, dangerous highway from Amman to Baghdad: "I told her that Baghdad looks like a great opportunity. Of course, she started crying."

Most contracts in Iraq have gone to big companies with political clout. But the billions have also lured some of the world's most adventurous entrepreneurs to one of the world's most impossible places, where insurgents with rocket-propelled grenades take potshots at hotels favored by Westerners.

"Everyone thinks we're crazy for coming to Iraq," says Larry Underwood, an American based in Paris who recently landed a contract to help outfit the new Iraqi army. Yet the 59-year-old calls Iraq the biggest opportunity for entrepreneurs for the next two decades. "Let the big companies have the big contracts," he says. "I'll be happy to take the crumbs."

Perhaps a bigger worry than security is adapting to an Iraqi business culture that's based on inshallah (roughly: "If Allah wills it"). Briefly, when an Iraqi says inshallah, it means he'll try to get it done. Sometimes it happens, sometimes not.

Brooklyn's Mirza sealed no deals during his two-week visit, although he made great contacts. "I should expand my mind about my business," he says. "These are the new areas I should be getting into." --BORZOU DARAGAHI