But, I'll also say, LPTHW is deceptively simple. Try doing it anyway, since if you know a language already you can blaze through it, and when you get to around 30 or so it sneaks up behind you.
Coming from experience with the last version, it definitely does sneak up behind you around part 30. The pacing and attitude for programming is the reason why this is one of the books I recommend to people starting to learn general programming. Specifically for me, however, I need something a bit more concise as when I'm in programming mode I tend to lose focus when there's too much fluff.
Try Dive Into Python 3[1] (although it deals with Python 3, it's more recent than the original Dive Into Python and a lot of what it teaches {to not say everything} is applicable to Python 2, and it touches on the potentially troublesome bytes-Unicode difference).
Don't let that stop you from trying the book. I started programming "way back when" in ASP/VBScript. These days we're a RoR shop, but I needed to pick up Python rather quickly for a side project.
LPTHW is structured well for beginners, but it just so happens it's structured well for pros too. The exercises are a great way to discover portions of Python that aren't intuitive to you. You'll hit roadblocks where your code won't run. That's when you'll really learn.
I would still recommend it, even to those who know how to program. A lot of the book is just non-stop typing as fast as you can. The benefit to me was how it improved my 'muscle memory' when actually sitting down to write something on my own. There was less stumbling over little things like -- "how do import a library again? 'require?' 'load?'"
As with most things, you get out of it what you put into it. For example, I wrote unit tests in one of the 'extra credit' assignments to explain a bunch of python's symbols.
Would anyone like to recommend something similar for people already well versed in (a) mainstream language(s)?