This is a glitch in FF
3.0.* that, to my knowledge has not been patched yet. Hopefully, FF
3.1 will work correctly. Simply using the "Clear Private Data" option will not clear your search history from your URL bar (aka "awesome bar"). Unfortunately, the only process I have found that works is to clear each entry manually. The way to do this is highlight the entry by placing your mouse over it and while holding the Shift key, press Delete. Be aware though, that in FF
3.0, the URL bar draws from your stored bookmarks so if you don't want to see a particular URL when you start typing an address, you will have to delete the bookmark as well. An example of this is, even after using shift+delete to delete the URL entry for http://www.airliners.net/,
if you have that site stored in your bookmarks, if you type "airliner" in your URL bar, FF
will suggest the airliners website as an option.