On rifles of .50 cal and larger, I like to start with at least 7/16" wood and prefer 1/2", tapering the rod quickly to the first pipe. I don't reduce much smaller than .350" for the rod tip on the small end (make my own tips) and this never jams in a 3/8" rod hole. I also use the small end to send the ball to the charge - never reverse the rod, so the bulbous muzzle end is easy on the hand for seating the ball.