I generally run about an ounce of 6s when I hunt. Pheasant and grouse season overlap in MN, and many of the places I hunt you can find both. 6s also lessen the "running around on the ground" factor for birds that are going to die, but, aren't just there, yet. And the "too many pellets in this bird" thing, which, makes 'em hard to eat.
Many years ago, I had a nice conversation with an English gunsmith, who told me he only used #8 when he went pheasant hunting. The conversation was more about loads for older English guns than hunting, so his load would have been more typical for clay shooting than any pheasant hunting I did. I tried a typical low brass load in the more open barrel of my McNaughten boxlock, with predictable results, ie, my Gordon spent multiple hours running down winged pheasants, that day. I went back to 5s and 6s later that afternoon.
On another conversation with him, I discovered he had never hunted pheasants in the US, and had only hunted birds that were driven to him, and birds that weren't all that wild, either. I feel guilty about shooting incoming birds I encounter in the wild, as they seem to die several magnatudes easier than those cagy birds that get up perhaps 35 yards out going straight away.
Grouse give up the ghost a bunch easier than do WMA wild pheasants, in my experience. I still use 6s on them. Force of habit, at this point.

Best,
Ted