Can I point my domain name to an Azure web site?

Question

In the current technical preview, Azure lets you create 10 ASP.NET websites. They are given domains such as http://yourappname.azurewebsites.net. Is there currently any way to p

Answer 1

As mentioned by Sandrino, this is possible only for reserved instances.

Not sure about Scott Guthrie answer. Check this thread.
It is stated that at this time there is no plans to support custom domains for shared instances.
It also contains a request to comment on Scott's answer.

Update:
It might be available for a fee (same thread)