How to remove a Verb for a Web Part?

My zone allows EDIT but, for certain Web Parts I have there is nothing that is user editable. For these I want to remove the EDIT verb/menuitem.
I've tried doing a me.AllowEdit=False/myBase.AllowEdit=False in the Render, Load, Pre-Render and Init events of the control but it never removes the verb.....
Any pointers?
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