There are a few different shotgun chokes that can be used for hunting small, fast, close birds. The two best choke tubes for this type of hunting are probably the Improved Cylinder and the Modified choke tubes.
Small, fast, close birds are usually shot at around 20 yards. One of the best chokes to use when hunting these types of birds is probably a “cylinder” choke tube because it will give you a more even spread pattern without too much constriction of the shot. It’s not going to be perfect, but it’s going to have a very even dispersal pattern of shot rather than being too open or having little difference in pellet sizes. In other words, it will concentrate more pellets on your target with fewer over-shooting pellets that may scare away whatever creature you were trying to hunt.
The Modified choke can also work well for this type of hunting because it allows some extra room for error on your part in terms of your distance estimation and shooting technique. So it’s possible that you will get a wider pellet dispersal if the Modified is used, but not by much in this situation.
One of the biggest things to consider when hunting small, fast, close birds is shot placement because you are using an extremely tight choke tube. It would be nearly impossible to use too tight of a choke at 20 yards so it really comes down to having enough pellets in your target area to ensure an ethical kill.
The only other consideration with these types of chokes is recoil reduction since they can be more difficult on your shoulder than normal, open choke tubes.