I've never done any dedicated woodcock hunting. Shooting them has always been a consequence of moving through woodcock habitat while either grouse or pheasant hunting. I'm sure my score on them has been much better when I am carrying a lightly choked 16 or 20 ga. gun for grouse versus a tighter choked 12 or 16 ga. that I'd prefer for pheasants.
All of my woodcock shots have been taken at shorter ranges, most no more than 15-25 yards. They are certainly a challenging target, and I'd characterize their flush and flight as closer to vertical than most birds, and often more of a spiral ascent into the tree tops than the zig-zag flight of grouse. Trying to track a flight pattern like that is near impossible, and requires more of an instinctive quick point and shoot. (strangely, the grouse I flush while deer hunting often seem to fly perfectly straight away, and I often easily track them with my open sighted flintlock, and swear I could hit them with a rifle.)
My Dad had but one shotgun, a 16 ga. 870 Rem. pump. He said it was choked far too tightly when he bought it, so after literally shredding a lot of game for a couple years, he took it to a local gunsmith and had a ventilated PolyChoke installed. It wasn't just a set and forget fixture. He frequently changed the choke setting as he moved from thicker cover to open fields. And he'd swap shells for a most suitable shot size. So when he was hunting grouse or woodcock in thicker cover, he would always set it to Cylinder or Improved Cylinder... or what he called his "Bushel Basket Choke".
When I shot some patterns with it years later, I was surprised at how consistent and effective it was. It was not just a gimmick. It produced nice even patterns that were variable at the turn of your wrist.
So for a dedicated woodcock or grouse/woodcock double gun, I would want "Bushel Basket chokes", i.e., Imp. Cyl/Imp. Cyl or Cylinder in the right and Improved Cylinder in the left.
