My very first horse was much like the dead broke you describe, lazy, and could be described as boring. (I loved him still though. He WAS a good horse for an 8 year old). Then when I was 13 I got my mare (my once in a life time horse). She was alot hotter than what I was used to. She'd never been ridden in her own 13 years of life (Atleast that's what I was told), She was a bit hard to handle, mainly because no one bothered to handle her, and needed a stud chain to control her, etc etc. As a 13 year old, I was probably in way over my head. Working with her every day, I finally managed to get her to be a good horse. Granted, for anything I couldn't handle, I had my father (a man that'd been working with horses for 40 or so years at that time) step in. After a year or so, maybe a little less, we took her to a fun show, and she did beautifully, we were in the ribbons in both of our classes. 3rd in equitation and 4th in pleasure.
I will be the first to admit that I honestly wouldn't want to repeat that experience, the top to bottom again if I had the chance to reverse it. She was originally too much horse for me, but with a bit of work, became the perfect horse for me. I will also admit, that my pariticular situation is *Far* from the norm, and should definitely be avoided. Now however, I am very confident I can handle a horse like her again on my own. (Note that we were both 13, the horse and I, and I am now 23, so that was over a decade ago.)