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Tele-zoom lenses all depend on F point 2.8mm is the standard for the good lenses and focus speed. Big role plays IS factor but only when you shooting from hand. When on tripod IS suppose to be off. If you talking about the lens that I think you talking about the F5.8, NON IS, 70-300MM then here is a few things about this lens:
Don't shoot from hand (no IS), use tripod, don't use it on moving subjects, the focusing speed is too slow, and don't shoot very long distances, maybe try from 15 to 25m. This lens also needs a lot of light, make sure there is a lot of light.
Try that!;)
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How I do it ...
When using my long zoom lens, I almost exclusively shoot birds in Shutter Priority mode and at as high a shutter speed as the camera/lens/light will allow.
As others have mentioned ... don't use a shutter speed that is lower in number than your zoom length. So 300mm means 1/300th absolute minimum. I'm much happier at 1/800 or higher if I can get it.
I've very rarely ever used a tripod for shooting birds. But I do have image stabilization.
I use a single focal point not the whole 9 points. I obviously try to get that single point on the birds eye.
I use AI Focus or AI Servo which are Canon modes for making the camera re-focus when it sees movement even after I've composed the shot.
I don't expect sharp photos unless my subject is reasonably close to me. I'd be happy to get that pelican of yours sharp at 300 - 400mm if that was as close as I could get. But at 300mm I'd want the pelican to at least fill half of the screen if I could.
Regardless of the shutter speed, the flash is very quick so I find it's helpful in stopping the movement if it's not going to ruin the shot or be effective at all.
I haven't found that a cheaper lens can't do the job. It may be a little slower on focus, and a little more soft at the longest zoom.