1. Select all and copy it to a new layer.

2. Working on this new layer I apply Filter > Noise > Median set at about 2 or 3 pixels. This blends the errant pixels with their nearest neighbours but does introduce some edges which are not wanted. To clear these edges I apply Filter > Blur > Gaussian Blur at 1 pixel.

3. Next to bring back some sharpness I Filter > sharpen > Unsharp Mask set at 1 pixel and 400% to 500%. This may sound drastic but give it a go...

4. In the Layers palette alter the opacity level of this new layer to allow the old image to show through and when you have got a pleasing result (probably 30-60%) apply Layer > Merge Down.

5. Now I apply the Unsharp Mask as I would normally and I find that it doesn't pixelate as much as previously.

Give it a try on one of your images which has problems and then apply Unsharp Mask to the image and to the original image which hasn't gone through this process. You'll see the difference in the detail. This coot had lots and lots of bright red pixels on his wings which ruined the shot, however, with this technique, you can salvage it somewhat.

Another interesting approach is to slightly alter the background noise with Gaussian Blur, as explained here by Alain Fossé. To do this in Photoshop:

1. Edit in Quick Mask Mode (Q)

2. Select the bird and its perch (and all the things of same level) with, for instance, PaintBrush Tool (B) (adjust the size of the form); the default selection will appear in red.

3. If needed, adjust the selection by erasing extra red with the Eraser Tool (E)

4. Edit back to Standard Mode (Q)

5. Inverse the selection to select the background with Select>Inverse

6. Apply on the background: Filter>Blur>Gaussian Blur: 3 or more pixels.

This is how the Common Buzzard (Buteo buteo) shown below has been modified by Alain Fossé.

Dave Curtis applied the same filter on this Starling (Sturnus vulgaris) to increase the 3D effect.He used another method however, as described below. It takes about 5 minutes and the final picture really looks better.

1. Open the layers palette (F7)
2. Drag the image thumbnail over the centre icon at the bottom to create a copy of the original.
3. Use Gaussian blur to blur the original layer.
4. Select the copy layer and add a layer mask, bottom left icon.
5. Use the airbrush to create the mask.
6. When you are happy with the result merge the layers and save as a new file.