How to tell bad quality sleep

I know when I'm either stressed or not that tired because I dream.

If I'm shattered, I won't dream. If I have things on my mind, I dream.

If my body's just taking the rest because it's lazy, I dream. But I don't just dream. My alarm clock woke me up this morning while I was dreaming about my Nan telling me what a great deal on interest rates her bank just gave her. She was actually reeling through the details. In my dream.

If your body doesn't really need the sleep, why not just let you wake up?!