Daniel Pipes present a compelling third choice between staying in Iraq and leaving completely. Basically, he proposes staying in the deserts, but leaving the cities to the Iraqis.
I don't think he goes far enough. I would make it even more specific: we should build significant and permanent American bases of operations (both Army and Air Force), and use them to stage military actions as needed throughout the Middle East. Our goal in Iraq should not be to solve the Iraqi's internal problems, but to ensure that no government or group can entrench in Iraq that opposes American interests. Maintaining bases would thus accomplish two objectives.
Should Iraq stabilize into a stable, secular government that recognizes individual rights, we can at that point establish formal diplomatic relations and negotiate the terms of retaining our bases. I certainly don't propose that we violate the sovereignty of any nation, but at this point, Iraq is not a sovereign nation.