YOURLS is free software to create short URLs for websites. It can be installed and run by everyone! This extension eases the shortening of URLs from Firefox. It integrates into the UI (toolbar button and context menu) and communicates with your own or a public YOURLS instance. Key features:

passwordless authentication
provide a keyword for the short URL
selected text on the web page to use it as keyword
automatically copy the resulting short URL to your clipboard

Permissions:

Access data for all web sites: The extension needs access to the current website to get the URL and potentially selected text (for keyword suggestions), and the extension needs to access any other URL to communicated with private YOURLS instances.
Input data to the clipboard: The extension is able to copy the shortened URL to clipboard (can be configured in the extension's preferences)

Read more at my website.