I did some patterning, and have shot a few wild pheasants, with the Federal 1 1/4 oz 16ga "magnum" (2 3/4"). Great patterns, but really painful to shoot paper with those things out of a relatively light sxs.
At one time, Remington offered a 1 1/8 oz load in its "Premier" shotshell line: 2 3/4 DE rather than 3 1/4. Those were good pheasant loads. The current 1 1/8 oz 16's are the 3 1/4 DE variety--and I've killed a pile of pheasants with those--including out of a pre-war Sauer that originally had short chambers (which I would never do again). In a gun with a bit of weight, pushing around 6 1/2#, and with factory 2 3/4" chambers, I'm not afraid to shoot those at wild pheasants. But they're enough for me, and I wish those old Remington Premiers were still available.