A bout of the plague

After doing a few test renders of Jim's animations, I've been plagued by these annoying black spots that appear on some frames. After doing some research, I've discovered that they're known as Final Gather artifacts. They also crop up in global lighting too. Anyways, I think I've now solved the problem by increasing or decreasing the amount of Final Gather rays and the Filter size in the Render settings. This however seems a bit like a lottery at the moment! There doesn't seem to be a clear method to preventing them, just re-render after re-render, testing to see if they appear; which is very annoying as each frame takes 2 minutes to render.

Examples of this plague:

Exhibit A


Exhibit B