I mentioned earlier that I was ripping my entire audio CD collection to my computer for ease of use. Initially, I was getting the back covers out by sticking my fingertips underneath the edge of the “tray area” (the part with the eponymous jewel), and then wiggling the tray to the side to dislodge one of the locking pegs from its slot. This has the side effect of really turfing up your fingertips after awhile, and so I did a quick Google to see if there was any Internet Wisdom on the subject.
As it turns out, there is. Seth Golub has a nice illustrated example of an easy way to remove jewel case trays. In short, you simply hold the jewel case from underneath, near the hinge, and flex the edges downwards (while pressing up from underneath the middle of the hinge). The tray will inevitably pop out, enabling you to easily access the back cover art (and, in the case of my copy of Kid A, the hidden booklet from the first pressing). This can be done very quickly, and with less time variation than prying the tray up (several CD cases were very stubborn in this regard, and required a couple of minutes to dislodge the tray).
I imagine this trick is probably common knowledge in record stores across the world, but it was new to me.