The source material that I'm using for the DVD is a set of illustrations that are finely drawn. The areas of the drawings that are causing the problems are those where lines are drawn very close together.
The rendered video looks fine on the computer but when played on a television, the shimmering/flickering in these areas is considerable. (Also, the illustrations are black and white but there is a faint hint of red or magenta in the flickering portion on a television.)

I have a suspicion that the source material needs to be altered to accommodate the poor resolution of tv. I hope that's not it.

Thanks for your help.

You can try to introduce a slight blur in your video editor, that will sometimes take out most of the jitter (called aliasing). If that doesn't work, then you'll need to magnify the original material. A little zoom in and panning may still allow the viewer to understand the illustration.

Line widths/spacing less than three or four pixels on DVD will usually alias on TV displays since they only have about 400 lines resolution on the screen.

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Software -Magix Movie Edit Pro 10, Nero 6 + NeroVision Express, Moho 4.61, PSP 8.1, Bryce, Quicktime 6.52 pro, Goldwave 5, DVD-Lab.
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smoothing/antialiasing should work, yep.

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That worked perfectly.

I just applied a very slight gausian blur to the affected frames and the shimmering completely disappeared. And there was no noticeable difference between the original image and the altered one.

Thanks again.