Right now, civil reconstruction efforts are caught in a trap. It is impossible to spend the money allocated by Congress in a timely fashion. There just aren't enough Halliburtons and local contractors to spend the money quickly enough.
The key is the government procurement process. This throws sand in the gears in the name of fairness and transparency. In a mature economy, the tradeoff makes sense. In a war zone, operators like Halliburton become key since they are not handcuffed by the regulations. Of course, there are always pricing concerns...but it ends up with a much better result than if a government contracting officer was trying to do everything.
But when it comes to building schools, running power plants, etc., the Halliburtons of the world are less effective. Security is awfully expensive. Sites must be carefully negotiated. The proper materials must be imported. It is very difficult to effectively use small businesses and locals (except as manual labor).
So flip the model on its head. We have money. We want results. The methods are irrelevant.
The solution is to post bounties. Distribute some general plans for a model school far and wide. For every one that is build to plans, cash is paid on the spot. Build it using local materials, build it in another country and ship it in, pray until it materializes from the heavens. However you can make a school appear, make it happen. The builder announces that it is constructed and requests a government inspector. If it generally qualifies they get paid. Perfection gets a bonus.
This encourages locals to get heavily involved in construction. To use their contacts in other countries. To accept the security risks of transportation. To use their influence to prevent bombing the school prior to the inspector arriving. Local materials are maximized. Local labor is maximized. You could even make things easy by setting up supply depots in secure areas where school building supplies can be bought on credit. And the supply depots can be stocked the same way -- let Iraqis use their expertise to have materials appear in exchange for cold hard cash.
And then you outsource running the school. Submit your registration list (use thumbprints to prevent fraud). If the inspector arrives and everyone is learning, has textbooks, meets class size requirements, the head of the school gets paid. If things aren't so perfect, they get paid less. In the worst case, they're shut down and a new set of principal and teacher thumbprints are necessary to get paid in the future. Cash is directly distributed to teachers using ATMs. Good grades on the national exam at the end of the year gets everyone a bonus. Students too. Paying students to go to school is a good way to force a degree of normalcy -- people don't stay in their houses if they're missing out on good money (enough to feed a family). Thus they're incentivized to use community pressure to keep things at least safe enough for kids to walk to school.
This model of bounties is akin to the way Andrew Carnegie built his libraries. $2/resident with the town agreeing to match 10% of the amount for annual upkeep. He built 2,811 of them.
Here's another idea. Give every citizen of Iraq $100 for civil works. It can only be spent by using your thumbprint to sign a petition describing the project. At the end, everyone on the petition votes whether the project was successful. The petition and voting would be done on a specialized ATM-style machine which would have proximity sensors to ensure voting privacy for each citizen. If citizens red flag the project at any stage (again through the machine) an inspector would be sent out. Otherwise the project leader uses a disposable digital camera (dispensed by the ATM at the end of the project) to document the project. After the pictures are reviewed, the ATM spits out cash to the project manager so suppliers can be paid (you could even do progress payments). These machines could be placed in even the worst areas to encourage some semblance of civil society (it would be hard even for Baathists to refuse cash on the spot).
You could get really innovative. Tired of power lines being destroyed? Pay people a cash bounty every day power is present in a town. Or the pipeline isn't destroyed. Or there are no terrorist attacks. Or no one is kidnapped. Incentivize local militias to form and patrol. Turn in enemy weapons, the militia gets paid. A high value target is captured, the militia gets paid. Every day of peace and quiet could put money in the pockets of every resident in the town. Some will just save it to attack Americans. Some will use it for their families. Some will invest in the future.
Yet our solution is Halliburton and six levels of subcontractors. Ten thousand ATMs spitting out cash in an incentivized fashion (with exploding dye packs to prevent tampering) could radically change the dynamics of Iraq.