
This Firefox add-on is very simple and do just one thing : it closes the current tab and "forget" about the visit. For that, it suppress the related cookies and, if configured so, the whole domain's pages from the history.
Close'n Forget is available in 5 languages : [fr], [en], [es], [de] and [ja]
Once installed from addons.mozilla.org (best - and only - choice, as you can't download it here anymore), the Close'n Forget add-on appears in the add-ons manager :
You must install the dedicated button
where you want, by right-clicking in any toolbar :
and dragging it to the place you want it.
For example, you can put it in the menu bar, like that :

Once you have the button available in your prefered place, and when you want to leave a website without keeping the cookies it has left in your browser, you just have to click on this new button.

Note that the button's background turns brown when the mouse pointer is near or above the button. So then you are sure to not confuse it with the regular Firefox's Close Tab Button.
When pressed, the button closes the active tab and remove all cookies from the internet domain of the closed page. The number of deleted cookies is displayed in the status bar :

Pretty usefull, no ?
With Close'n Forget, you can do even more !
You can also remove the visited site from the browser's history. To do that, simply go to the extension manager and open the Close'n Forget options dialog

Then check the only box, and confirm, like that :

The next time you will close a tab with the Close'n Forget button, not only you will delete all related cookies, but also remove any reference to the current site from the browser history.
Like that :
Enjoy !