Right. Although it wasn't clear what exactly they meant by using a CNAME. They could have cleared it up greatly by saying using a CNAME to the official DNS name of the elastic IP, i.e. ec2-75-101-137-243.compute-1.amazonaws.com.
You can also use the internal IP address of the machine. i.e. with Windows instances if you do an IP Config you'll see an address to the effect of 10.X.X.X. Instances in the same availability zone can communicate with one another using these IP addresses without leaving the network. This saves dramatically on costs and performance.
At some point I need to write a little script that lets you launch with a "shutdown after" somehow. I blew a couple hundred bucks on forgotten machines once. Oops.