For close to 20 years I used a Navy Arms SxS 12 (the Pieta version) with cylinder bores for snowshoe hares over the beagles we were raising and training. Distances will vary from place to place, but I had to be awfully careful with 1 1/8 oz loads not to pattern the hares, or pay the price in mess. At first I dropped down to a 1 oz charge and finally to a 7/8 oz charge. Then I settled back on 1 1/8 oz for pattern density at the ranges I needed, but with #4 or #5 shot to limit the number of strikes, while also using the edge of the pattern to "fringe" them.
I traded off the old double when steel shot requirements finally came to Alaska (it was my principal duck gun too), and regretted it ever since. I got an identical replacement recently and that's put me back in the rabbit business. I still won't pass up a cylinder bored 20 SxS or especially a 410 SxS when I come across one at the right price.
Earlier this winter before getting the NA double I was using my Renegade with a 62 cal (20 gauge) GM drop-in barrel and 7/8 oz of shot. I was out of the larger shot and had to use #6, and I still had to fringe them with that load all the way out past 30 yards. I doubt I'll be using that combo much any more, because it actually weighs a fair bit more than the NA double 12.