I have done this only once. I had been upgraded to a pretty nice room, which was currently going for a lot more than I was paying. The lowest room available on the website was cheaper than I was paying. I called the front desk manager and asked about the logistics of checking out in the morning, and moving into the cheaper room. She put me on hold and then said that I could continue to stay in my current room for my current rate, which was really my preference anyway.