What MacLeech has just written is only part true.

Although he does make some good points in the above post.
CREDIT FOR THE FOLLOWING POST COMES FROM THE ORIGINAL POST BY MACLEECH.
The assigned IP address will be given back to you even after it's expiration time as long as:
1. The equipment requesting the IP has the same MAC address.
Response: I've never had a problem with getting a different IP address on the same MAC address. So, I'm not sure how much this makes a difference but for me it doesn't seem to matter.
2. The IP address previously assigned wasn't issued to another client during the time it was released. (This rarely happens unless there is a major outage, a shortage of assignable IP addresses, or the client released the IP for several days.)
Response: This doesn't seem to always be a problem for me but he does have a good point here! If that IP address doesn't get taken by someone else, there is a 50/50 chance you might get the same IP address or a different IP address.
So IF you want to change your IP, the easiest way is to change the MAC address of the device requesting it.
Respone: Never done this before but have read plenty of posts that it seems to work, but I've read that it only seems to work one time so I've heard around the forums on www.dslreports.com So....do some research and experiment with this one.
Now as far as the process I posted in my post, I released my IP address at 5:16 PM Eastern Time and then renewed it at 6:16 and I got a new address. Before my IP address was 208.120.52.9 and now it's 208.120.52.XXX (Those X's represent that now I have three numbers in the last set instead of one.) So experiment and see what your results are as I made in the original post.