There's a method of peeling mandarins where you remove the top and bottom of the peel, then just "unroll" the rest into a long chain of separated segments. It looks neat, but I think that's about where the advantages end. For me, the problem with peeling a mandarin isn't the presentation of the finished product, it's the juice. If you have a mandarin that's just a bit soft, you're going to end up dripping some juice around, regardless of how you peel it. I've tried this "caterpillar" unrolling method, and it doesn't seem to result in any less juice. I still have to dig my fingers in and put pressure on the segments to separate them in that configuration, so they still get slightly squashed and release juice. I'll probably continue to do it this way, but if I hear of another way that promises to reduce the juice, I'll try that.
Mokalus of Borg
PS - If you tell me some method is called "flaying" a mandarin, I might pick it based on name alone.
PPS - But then I'd feel self-conscious saying it to anyone.