From the reviews I have read, this lens tends to be a little soft, especially at the 200mm end. This tends to be a characterist of most zooms, which is one of the reasons many recommend primes.
As Drifter suggested, make certain you keep the shutter speed up. A good rule of thumb is for the shutter speed to be a least 1/x, with x being the length of the lens. You should also take into account the “crop factor” of you lens, which on the 20D is 1.6x. So the 200 becomes 320mm and the shutter speed would be 1/350 or 1/400 depending on whether you have your camera set for 1/2 or 1/3 stop increments. On the 20D you can push the ISO to 800 or even 1600 if you need to in order to keep the shutter speed up. The 20D does a great job of keeping the noise level down if the picture is properly exposed.
Another thing you might try, if the subject and light allows, would be shooting with the lens stopped down a little. Many lenses are not at their best when wide open.