I've developed a rather subjective way of looking at the J/P dichotomy. The way I see J is as being less flexible about the way you deal with things. It doesn't really matter if you're organized, as much as it's about your need to have a certain structure in the way you behave. For instance, my home is usually a mess unless there's a possibility I might have people over, but I keep my definitions, rules, and ideas in good order. Also, I'm quite particular about my spelling and punctuation. That's another common J trait.
Lastly, I'd like to introduce you to an idea that a friend of mine had. He believed that J's think symbolically, which would mean through words/numbers/icons. P's on the other hand, supposedly think graphically/visually, which would explain to me why their thoughts seem to be less fixed, like a movie that changes scenes from one moment to the next, and mine are arranged more like a book. I can't verify this idea, but it seems at least plausible, since interpreting reality through words, which point to things in a more specific way than pictures, would lead to slightly more predictable and rigid behaviors.