Bit.ly is becoming more liberal with invites into their Pro service. One of the things Bitly.Pro provides is the use of a custom domain for shortening links. Most hospitals refer to themselves, internally, with initials. Some State Regional Hospital is probably SSRH internally. There's a good chance you can register those initials or a close variant. It makes a nice way to keep your tweeted links aligned with your brand.
Bit.ly, and Bitly.pro also allow you to create custom short names. When you combine a custom domain and short name, some even neater things happen. Rather than saying "find us on facebook" you can use a link like ssrh.biz/ssrhfb . It makes a nice way to send links internally as well.
The waiting time for a bitly.pro invite seems to be less than a week. In addition to the custom domain, they also provide some enhanced, detailed reporting tools. Check it out at the Bitly.Pro site.
As for me, I'll be posting links via Daws.in (because .on isn't a valid suffix and I was all out clever).