All the carp, suckers & redhorse we get we smoke. You take a cup of pickling or canning salt per gallon of water and a 1/2 cup of brown sugar to make the brine. Cut the fish in half (leave the head on and some women will not eat them.. more fish for me), wash it out good, and be sure and clean the mud line out of the fish located on the top part of the fish, inside, under the fin. Take a spoon and scrap it clean and then wash all the brown out of it before you brine it. No need to scale the fish as after it is smoked, you can use the skin as a plate if you like.
Soak the fish totally submerged for about two to three days. After that you can rinse them in clean cold water, ONCE. From there let them sit 1 hour at room temp and they will firm up. Now go and get your smoker going with some heavy smoke. Maple, apple, hickory are all good woods, even popular will work but does leave a special flavor you have to like. Avoid oak or wild cherry and no conifers like pine or balsam wood at all...
Smoke them in hard hot smoke with the fish on racks (old refrigerator shelves make up my smoke racks, and they rest on hickory handles). Smoke them as moist or as dry as you like (I like them smoked dry). After they are done, we vaccum seal them (if we can not eat them as fast as we make them) and freeze them for smoked fish at a later time.
We did pretty good on the Redhorse this year. Caught some big ones in the river actually. I had a great time when I had a large one on an ultra light set up. We really went around for a while.
But to throw them on the bank to rot... NEVER!!