I don't know about baby bunnies, but for adult cotton tails I use a magazine rifle chambered for the 375 H&H. 270 grain hard cast bullet loaded to 1300 fps. Drills a neat hole and doesn't spoil any meat. The 375 H&H will produce very fine accuracy with lite loads, something the various blown out and improved 375s do not. Bottom line, if you can stop a charging cotton tail with a 375 H&H you will be able to hit something bigger.