Back IS Close replaces the "Back" button with a "Close" button when the "Back" button is disabled because there is no page to go "back" to. That Close Button will close the tab or browser, as appropriate.
Back IS Close is the perfect complement to tabbed browsing: it closes the many tabs tabbed browsing opens. Back IS Close works most effectively when you map a mouse button (I use the right mouse button) to send "Alt-Left Arrow". Then one mouse button will either take you back to the previous page, or close the tab if no previous page exists, making for quick, convenient browsing.
See the full documentation, including the privacy notification, at author's homepage: http://www.diffenbach.org/back-is-close.html
If you have questions or issues, please read the author's homepage for the extension.
IF YOU FIND A BUG, please email me, as I don't regularly read the comments here; emailing gets a faster response, and I can work with you directly to debug any errors. Email me at back-is-close AT diffenbach.org
If you want to discuss the Back IS Close extension, do that in the Mozilla extension forum, in this thread:
Users of the IETab extension should see this documentation page: http://diffenbach.org/back-is-close/back.is.close.ietab.html