Clearing all of FIrefox's history doesn't have to be for all websites—you can remove them individually instead.

When you delete your Google search history, you remove all sorts of information that could potentially be used by shady characters. Beyond the funny videos, news stories, trivia, and other content ...

Select History from the menu. Choose Clear All History to view available options. Select the data you want to remove by checking the boxes (e.g., browsing history, cookies, cached data).