Add; change 'search engine' treeview, to the address bar right click context menu.
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If the option to search from the address bar is enabled, show an option to change the search engine in the right click context menu. If the option 'search from the address bar' is not enabled, hide the option. It's simple, unobtrusive, intuitive, and in most cases , would eliminate the need to have the secondary search field visible. Just a thought.