All carp I have caught (more than 30, less than 50) have been on 8wt or heavier rods. I usually fish the Red River in Manitoba for them, and as such, presentation isn't as important as the fly being right in front of the fish's face. I would imagine the following works on clear waters as well, but I haven't successfully tried it with carp as yet.

I short cast to the fish using a weighted nymph (prince nymph is my most successful), and let the fly drop to the bottom in the carp's feeding lane. I will then lightly jig the fly as I slowly retrieve it, similar to the gear fishing tactic of jigging, but on a much smaller scale. I would create the jigging action with short, quick line retrieves (4 inches at a time) rather than with the rod tip. Make sure you wait to let the fly drop back to the bottom.

I use a heavier leader such as 12lb fluorocarbon and it doesn't seem to hurt. Using this technique gives me a pretty good connection with the fly, and I can usually tell when the fly has been taken. Make sure your fingers aren't near the reel handles. I have had mine smacked but good on one occasion.