If you are like myself and have an alternative or shorter domain name that you would prefer to use for the built-in WordPress URL shortening service, then this may just be the perfect plugin for you.
The Custom Shortlink Domain plugin was committed to the WordPress Plugin Directory today (2012-04-07) and provides the ability to override the domain name used.
Once installed, you can enter your custom domain via the Settings > Permalinks page by entering a value for the “Shortlink Domain” field under the Optional section.
In order for the custom domain to work, it must be pointed at (or parked on) your site, for more information on how this can be done you should contact your hosting provider if you are unaware of the process of doing this.
For full instructions on how to use the plugin or for more information visit the plugin page, or submit a post to the support forums for help or bug submissions.