I've looked into nutria hunting in Louisianna. It seemed to me that there is no mystery in why Louisiana is overrun with nutria. The regulations for hunting them seem to be at least as restrictive as hunting game animals in many states. From reading regulations I got the impression that they must have a poaching problem that they don't want to compound by having an open season on nutria with people running around with weapons capable of taking any size animal they might encounter while "nutria hunting".
Out of state hunting license aren't cheap either but that is true for most states.

eshell,

Check out "Insomniac" with Dave Attel on Comedy Central. He's a comedian who goes around to different cities and stays up all night. When he went to New Orleans he went for a ride with some cops out Nutria hunting. Setup was exactly what you described. At one point they all get out and let loose on a big group of them, rapid fire, real carnage. It's a great piece of footage.

Just got a package from the LA Fish and Game.......what a hassle......must apply to each individual area you want to hunt with a different application ....you then have to submit a IRS Tax Form????????????????? I think that you are all right.....to much trouble.....I just wanted to take a few days and try it instead of P.D. shooting.....thanks for all the help......Hal

In south Arkansas we stalk them much like early squirrel hunting. Just slip around the edge of sloughs and creeks and emit a very low moan. They respond to these sounds. I hunt with a subsonic .22 but have been known to take a few with the shotgun in duck season. Just shoot in front of his nose about 2" to avoid damaging the fur. The meat is very tender and tastes alot like chicken. ENJOY!! Crowcommander