Bitly plugin/link shortener alternative?

I’ve been using Bitly’s link shortener plugin for years to automatically create branded short links each time a post is published. I received an alert yesterday that the plugin has been removed from WP, so I need to find a new solution. The only requirements I have are that it:

• works with my custom (branded) domain that I use exclusively for short links
• generates a new link with each post (that I can pull from the post editor)
• can create custom links if I need to (e.g. /sale rather than an alphanumeric string)

I have a small budget to work with, so I’m not against a paid service. Any recommendations are greatly appreciated.