How to edit links?

From Manage URLs page click Edit Link icon near the link you want to edit.

Either side (short or long URL) can be changed as needed. As well as other properties of the Link: "Send Stats", "Protected", "Archived" etc.

NOTE: if your domain has been set for 301 Permanent Redirects and you tested an edited URL and destination appears unchanged it is due to your browser's cache. Browsers take shortcuts to perform faster. Rather than check the TINY site to verify if anything with the link has changed since its last use - the browser assumes it has not... grabs a previously written copy and redirects using your computer's local storage - bypassing TINY servers (and incidentally bypassing stats collection). In other words the link works fine for others who click it, but appears unchanged for you, until you clear your cache. Try clearing your browser cache and cookies
307 is a temporary redirect and will not trigger caching.
302 and 303 will not trigger caching either.
Redirect settings can be found under Settings > Account.