Suggestion: Private Tab
What it is: Instead of having a whole window for surfing private, the user should be able to open a private tab in the same, normal, browser window.
Why this would be useful: Sometimes you just want to do something that does not save cookies, history etc, but don't want to open a new window. If you want to browse private totally for a while, private windows can be good, but if you just want to quickly open a tab, private tabs are better.
How it can be implemented: Like it was in Opera 12. The favicon could for example, like in Opera 12, be replaced by a private-browsing-icon.