OK, I'm a coward. After dropping it a couple of times already (no damage) I ordered the slimmest case I could find that should still offer some protection, and maybe not add much bulk:
http://www.amazon.com/gp/product/B00O18HF14/
It didn't help that my brother visited today and told me horror stories about how many times his wife has broken and lost her smartphones. I also set a password for the device, something I don't usually do.
Really happy with it so far, it is living up to the hype for me. Hope you folks are enjoying your Fire tabs.