Apps similar to OpenInPrivate include Forget Tab, which is free. Other options are Forget that page and Incognito This Tab. In total there are three apps like OpenInPrivate for Mac, Windows and Linux.
Forget Tab is a simple and very lite Addon to easily clear history, cookies, storage and other info from current tab. Just click on the toolbar icon to clear desired items. A notification will show you what is cleared from current tab.
With "Forget That Page", you can totally delete the current webpage from your browsing history, just in one click ! It also deletes cookies, session storage, local storage and download history for that page.
Open current tab in an incognito window. Use its toolbar button or the context menu option to open the current tab in a new private window.
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