I spend a lot of time trying to take photos of small birds. The small warblers are so beautiful, but they move around so fast- it is difficult to get a good shot. I gave up trying to shoot these small birds with my camera and lens mounted on a tripod. I'm having more success using a hand-held Canon 400mm f/4 DO ISM 2 prime lens, with a 1.4 tele extender. It weighs 5 lbs- much less than my 600mm prime lens. It's important to keep the shutter speed to 750 or greater to get really sharp photos. I use manual mode- in AV mode the shutter speed drops too low. A shutter speed of 750 or greater will require a high ISO to get the proper exposure in low light. This introduces too much noise. So much noise that I'm often unable to correct it with post-production techniques. B and H photo makes a flash bracket that fits on the camera and extends the Speedlite flash above the lens. This is necessary to prevent "steel eye" in the bird eyes. Once I get this bracket and flash set up, shooting hand-held in low light won't be a problem.
Another problem is deciding where to set the focus limiter switch. Sometimes it needs to be set at the closest setting,if the bird is close- if the bird moves away you miss the shot. The Full setting includes the minimum focus distance to infinity, so the will work for all ranges, but autofocus is slower. I'm always trying to decide what is best. Small bird photography is challenging, but so rewarding when one gets it right.