The thing about 3D CG is it usually is rendered on black with a precisely-fitting alpha channel. We typically call this "premultiplied" CG.
Suppose you want to cut and paste it onto a background using Photoshop.
Here's a workflow which preserves soft edges and avoids matte lines.
The wrong way goes something like this: you load the alpha channel as a selection, cut the CG off of its black background using this selection, and paste it onto a background image.
Do that and you'll end up with a gray matte line around your solid edges, and a gray haze in your motion blur.
Let's try it a different way.
First, create a new layer above your beauty pass and fill it with pure black.
Next, Use the alpha channel to cut out this black color.
Now paste this black color directly onto your background image. In this example, the background image is a blue sky.
In the old days of optical printing, this technique was called creating a holdback matte.
Return to your beauty pass. Deselect the selection and dump from your beauty pass this newly created black layer. You don't need it anymore.
Finally, Grab the entire beauty pass, black background and all, and paste it on top of the blue sky-with-holdback matte.
Use the LINEAR DODGE blend mode. The LINEAR DODGE blend mode is arithmetically equivalent to a simple ADD. You are now performing what the optical printer guys called a double exposure or "DX" or burn-in
If for any reason your beauty pass is not aligned with your holdback matte, simply nudge it into place.
Voila. Perfect compositing of premultiplied 3D CG in Photoshop.
Here's the "wrong way" once again, for comparison.
So... LAYER > MATTING > REMOVE BLACK/WHITE MATTE is the official way to go.
If the official Photoshop workflow is giving you good results, then you are all set. If for some reason it isn't quite working (People seem to have mixed results on this issue) then here are some additional ideas:
First read Transparency Mapping and Matte Lines if you are not familiar with the idea of dividing the rgb of an image by its own alpha, and why you might want to do so. You'll even find a (last resort) method using Maya for doing so.
Next, consider undoing the premultiplication in your own particular case by using After Effects (if you have it) and John Knoll's unmult (free plugin) to render one frame.
Or if you have Shake, you'll find the necessary division node there.
Finally, you might try The Gimp. I understand it has a divide blend mode.
If you know of other methods for dividing in Photoshop, or elsewhere, I'd like to hear them.
btw - 'screen' is not literally the opposite of multiply; it is not identical to 'divide.'