Better yet, delete the entire search history and turn it off.
Edit: grammar
History is important, but the site is called "ruinmysearchhistory.com". I visit websites I know with my normal window, the rest is mostly in incognito and if it's something I want to remember, I'll make sure to include it (i.e: visit it in normal mode, Evernote, Bookmarks, email to myself, etc).
IE has some kind of private browsing option as well, but I don't know what would be the equivalent way to invoke it.