Perhaps as or even important is to not make what I consider the two classic mistakes oft made for visible in-coming targets:
1) the tendency on the part of some to mount the gun early and that leads to inevitable 'tracking' of the target and a near guaranteed miss.
2) waiting until the bird is past being in range and then it is a very rushed & jerky move at a too late moment for a well executed shot.
Both of these situations can easily be observed/demonstrated on a skeet field on station 5 high house targets. I think the 'trick' is to not move or mount the gun until the bird is in range .. and then it is a mount & shoot just as the gun touches the shoulder pocket in one smooth motion whilst keeping the bird firmly in focus at all times. That to me overides and negates any need worrying about the choke. Only AFTER you have seen the first bird hit [fall, in the case of a dove] should you move your eye to the second bird, should there be one.
In the same breath, if two or more birds are coming in taking the rear most bird first will many times keep the other bird or birds from flairing. Of course, if they have been repeatedly shot at then they will be more wary and may flair at the report alone. Hope something here helps.
