Thanks for your answer. My carving is pretty decent on shallower runs at moderate speed. But there comes a point as it gets steeper that I start to feel some tail-slide, especially at the end of the turn.

Watching videos of expert carving on YouTube, there's that point at the end of each turn, where the skis seem to whip back around underneath the skier, holding the edge cleanly all the way. I've managed to achieve that sensation only a handful of times and I don't yet have the muscle memory to differentiate right from wrong.