I think it might be a good idea to have a URL-shortening service for each of the Stack Overflow family of sites.
Since questions, and answers all have a unique id, it should be fairly easy to use that for shortening the URLs.
For example: (Could easily be shorter)
http://short-SO-url.com/1234
This could easily point to a question, or an answer. All this would need to do is redirect to:
http://stackoverflow.com/questions/1234
Or if it is an answer, point to:
http://stackoverflow.com/questions/{question-id}/-/1234#1234
You need something between the question id, and the answer id. That is why there is /-/
in the URL.
Right now, if you want a shorter URL, you have to use a third-party URL shortener which can point to anywhere. It is also difficult, or impossible to know that it doesn't redirect to a malicious website. If there were an official URL shortener that only worked for Stack Overflow, you would know for sure that it is safe.
This would be easier if there was an internal interface to redirect to the correct URL.
http://stackoverflow.com/api/post/1234.301
It could redirect to the correct URL regardless of if it is an answer or a question. 301 redirect
Don't
post your own ideas for the domain name here, someone could register it before the Stack Overflow team could register it. If you really feel strongly about a domain name, send them an email instead.