If left to its own devices, Firefox lets you open a private window for Web browsing on the sly, but the browser does not extend such functionality to new tabs in your current window. If such flexibility sounds appealing, then the Private Tab extension for Firefox is just thing for you.
The extension couldn't be easier to use, though you'll need to be running the latest version (20.0) of Firefox for it to work. Private Tab doesn't require a restart and simply installs a new menu item on Firefox's File menu (on a Mac, anyway).
With Private Tab, you now have the option in Firefox to open a private tab in addition to a private window.
In related news, if you worry about leaving private browsing windows open by mistake, the PB Exit extension I covered last month can help.