I suspect Dan and Jay may be on to something in their comments on this previous post. So I've been looking for an alternative rigging for the dry/dropper combo and found the below video. Hopefully this will result in fewer misses on the dry fly since the nymph dropper is not tied to the hook bend of the dry as with the traditional rig that I've been using.
In any case, I've noticed I get a little queasy when I'm tying that dropper on to the dry fly hook. I realize now that I don't trust it. A trout taking a dropped nymph is one thing, but a carp is an entirely different ball game. I can't get past the feeling that I'm asking for trouble. The below appears to be potentially a better alternative: