Aim low and let go...
We have quite a large problem with the carp in my neck of the woods. They tend to overeat the available bottom resources and put a strain on the other species we prefer to fish for.
I've yet to find a better removal method than bowhunting them.
The bowfishing rig is inexpensive and once you get the hang of it you can pull them out hand over fist.
Although some folks might not think this method is very sporting, I would like to note that I did in fact spend quite a lot of time trying to intice them to take a fly...and had ZERO luck.