While I have only been to Africa twice, I never recall wishing the hole in the muzzle of my rifle was smaller. Now I was not on the kind of hunt that allows you to shoot many shots each day, so recoil was not a factor.
I get the same feeling walking out in the dark when hunting around Yellowstone NP and cutting bear tracks.
There is always a bunch of .375 ammo rattling around a safari camp, if worse comes to worse.
