IIS7 AppCmd How To Set Application Pool of Site using XML

Question

I'm trying to determine what the correct XML is to tell AppCmd to set a Site's application pool correctly. So far I've tried:

<appcmd>
  <SITE SITE.NAME="~name~" Site.ApplicationPool="~name of existing apppool~" physicalPath="~path~" SITE.ID="17" bindings="http/*:80:~domain~,http/*:80:~domain~" state="Started" />
</appcmd>

But the site always is set to the DefaultAppPool.

What's the correct XML to have this be set correctly? I can only find references on how to do this from the command line, but I need the XML solution. Thanks!