Eradication
I agree with Kevin. To me, the notion of ridding the world of Hezbollah sounds just delightful. And if I thought that Israel could push a button or launch just the right series of military attacks and then be able to wipe their hands and know, well, we're done with that problem, then I'd be all for it - and would be willing to withstand some damage being done in the process. But this idea has about the same relationship to reality as befall dreams of ridding the world of "terrorists," or, I'm reminded of the constant local police refrain that we will now--for our next trick--root gangs out of our high schools. (Here's a newsflash: all it takes is a couple of disaffected teenagers angry at some other disaffected teenagers and you've got yourself some gangs. Good luck curtailing that.)

You know, they don't have printed team rosters or a limited physical quality or a precise chemical makeup. It's not like ridding the world of polio. It's like saying we want to rid the world of angry hate. You can't change just one thing. And the way you go about addressing it affects the shape, makeup, motivations, determination, resources of the other. I just don't think going after it with a bigger, more heavily-armed version of angry-hate is likely to work.