Windows 7: How do I clear this list?

Recently, I tried to create a new shortcut on the desktop, and was presented with this dialog. Nothing unusual about that, except that when I started filling in the field, I was offered some suggestions that, frankly, I'd rather not have other users of the computer see. (Honestly, I don't see why this box uses a history list, since it's unlikely that anyone would want to use the same URL more than once to create multiple shortcuts, but that's neither here nor there.) I went poking around in the registry, intending to clear this list, but I couldn't find it. Does anyone know where this information is stored?

Control Panel--> Internet Options --> General Tab --> Browsing History

Okay, that's the sledgehammer way of erasing everything (which, I'll admit, I would have never thought of because I never use IE), but where's the scalpel? What if I don't want to erase everything in the list, but just remove one or two entries?

Open Internet Explorer, Open up the History/Favorites , manually find the two entries and delete them.

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Jerry