how to remove / hide site actions and other ribbon options from annonymous access users and read only users in sharepoint 2010

I am creating an IT support site for our campus and I would like to be able to hide / remove the Site Actions drop down, page, publish, etc. from users who have annonymous and or read permissions on the site. I've gone through and tuned permissions down as much as I can but I just can't seem to get rid of everything I want to hide.
EITCAsked:
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EITCAuthor Commented:
Will this solution work on Share Point 2010? Just making sure. Thanks for the quick response!
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chapmanjwCommented:
I have not tested it in 2010, however it is a simple change to the master page that could be easily undone if it doesn't.
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