What I wanted was to transfer all the books which I purchase from Amazon from one Kindle to the other. I assume they all have DRM. That's not the point. The point is that they don't have a mechanism to do this other than one at a time. As far as I'm concerned this is yet another serious deficiency in their book management and organization. As much as I adore my Kindle, I believe that if Amazon doesn't come up with a better way to organize ebooks, some other competitor will. At the very least, on the PC at Amazon.com, I should be able to select multiple books from my own ebook collection and download them with a single click.
Why am I bothering to write this? For one thing, in case someone else wants to do this, they don't have to waste their time with customer service on the phone and also in the feeble hope that someone at Amazon will read this and suggest that perhaps they should make a few improvements? After all, they want people to purchase more books. The more books you have the more critical it is to be able organize them.
Three cheers for Calibre for tackling a lot of the problem. Sadly it doesn't help with this particular one. But that's not their fault.