Been looking around some and finally saw the first nutria in Joe's Bayou so far this spring...and shot it. Was it the tuned/scoped European HWs: R10 .177 @900fps, R9 .20 @780fps or the R1 .22 @790fps that stopped his swimming with a single head shot? No. It was my recently acquired, well used, all American, 1969 Benjamin 342 Tootsie Roll handled pumper with open sights!
I was standing on the Wise drive over about 3/4 of a mile east of the house shooting at sticks and leaves in the water when a small nutria surfaced out of nowhere about 20 feet right in front of me. Only had 6 pumps in the Benji so I watched it swim into the culvert. Pumped two more times as I crossed to the west side of the 3 or 4 foot high by ~15 foot wide one lane dirt drive over but didn't see it swim out!
Checked the east side again. Then back to the west side and a moment later it swam out from the brushy bank with a mouth full of green weeds trailing. From about 20 feet away I aimed between the eye and ear on its left side and pulled the trigger.
With a solid thwack the water rat dropped its snack, rolled onto its right side and spastically kicked the hind legs for a couple of seconds until its head bumped into some shrub stems that stopped its forward progress. I pumped/loaded the Benji while changing position to get a clear view between the stems of the shrub and delivered a second shot to the brain pan ending its agonal kicking. Hope this is a preview of the rest of the nutria 'season'.
Been shooting my couple of Benji 342s ('69 and LN '74) for the last couple of weeks and really enjoying them. So much so that I have ordered a freshly resealed '70 Sheridan Blue Streak to try the .20 caliber. Never had these as a city kid. Maybe that's a good thing.

Terry in LP