To me, Iraq was a fatal strategic mistake. If we were truly going to attempt "nation building" and wanted to send a message to the rest of the Islamofacists, then we would have chosen Iran as our target.
I have my own opinions of why our duncecap president chose Iraq, but it's not as simple as oil--like so many claim.
Iran, on the other hand, had a infant democratic movement and a general populous ready for upheavel, in my opinion. Since we invaded Iraq, that has retrenched and been retarded by their new government. Our move into Iraq actually played into the Ayatollah's hands in my opinion. It gave him fodder to work with.

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I am not saying I have an answer, but the most we can hope to accomplish at this time is to minimize casualties. Am I right on this point?

While certainly a noble goal, it isn't always a possibility given the tactics that terrorists use, and the war that we and Israel are forced to fight because of it.