While doing bird photography I usually shoot in Case 2 Autofocus mode. Case 2 is actually supposed to continue tracking the subjects, ignoring possible obstacles. I found it reasonably good option for bird in flight with sudden obstacles of tree, twigs and branches. Here is a fairly good shot taken with this option. In the month of August 2014, while roaming in Renusagar hill I saw a black shoulder kite hovering in the sky, suddenly it plunged into the bushes and came up holding a prey. I managed to take this shot before it vanished behind the tree. In the photographs you can see the bird has passed through some of the twigs, even then the tracking and focus was maintained on the subject.
Black shoulder kite holding its prey, Renusagar hill, India, August 2014