I understand I cannot register 2 character domain names, but why does it appear that there are no 3 character domains available either?
Some 2 character domain names were registered (eg bt.com) but two character combinations are now reserved for national top level use. 3 character domain names are available but, due to their popularity, most .co.uk and .com combinations are already registered. However, you may still be able to find an appropriate 3 character domains in the .uk.com or other domain. format