Piping a MySQL database from one server to another

I know that there's a lot of great, wonderful things that can be done on-the-fly through SSH. It's one of the greatest tools out there for moving data or communicating between two machines. So I thought "Why not try to move my database in the fastest way possible via SSH?", and here's the command I found :

mysqldump -ux -px database | ssh me@newhost "mysql -ux -px database"

This is of course a very basic, stripped down version of the command, which I haven't tested yet, but it's a good start to what seems to be a very common problem among developers.