You can temporarily switch to Private Browsing mode if you select Tools > Options > Privacy: [[X] "Automatically start Firefox in a private browsing session" That will enter Private Browsing immediately without a restart but in all tabs ans windows that are currently open. You can access the website and leave the Private Browsing session if you remove that check mark. You are in Private Browsing mode if you see "Tools > Stop Private Browsing" and all cookies made in the regular session are not available (see Tools > Options > Privacy > Cookies: "Show Cookies") but are restored if you close the Private Browsing mode session by removing the check mark in "Automatically start Firefox in a private browsing session".

Yes, all this I know, but I may have been unclear with my question.

I find it annoying to have to not be able to have "normal" tabs open as well as "private" ones at the same time. Is this something that can be achieved in any way?

At the moment I have to choose between normal mode or private mode.

The Private Browsing Window add-on does almost exactly what you want. I would use that.

However, it only opens a new window that is in Private Browsing mode. You can't just open a Private Browsing tab in the same window as regular tabs.

Thank you, that works great!

You can open a secondary profile (or even a different version of Firefox) if you pass the parameters -p and -no-remote to the firefox executable:

firefox.exe -p -no-remote

-p allows for selection of a profile, and -no-remote indicates that the starting process should not attempt to comunicate with an existing running instance of Firefox. That way, you'll have two instances of Firefox (with a different profile on each one) and you can put them on Private mode independently of each other. Not as convenient as Chrome's Incognito, but at least you can have a "normal" session in parallel to a "private" one.

Please don't dig up 12 month old postings where the "OWNER" said a suggestion "works great!"