While useless, this is nearly free in terms of storage cost in GIF files. So do yourself a favor and crop off any border before JPEGing. This will give you a chance to re-do the conversion with a higher quality setting if necessary. Gray-scale photos usually convert without much problem. When using cjpeg, be sure to use the -gray switch.
Color images are much trickier.
Smoothing averages together nearby pixels, thus approximating the color that you thought you saw anyway, and in the process getting rid of the rapid color changes that give JPEG trouble. Proper use of smoothing will both reduce the size of the compressed file and give you a better-looking output image than you'd get without smoothing. Values of 10 to 25 seem to work well for high-quality GIFs. GIFs with heavy-handed dithering may require larger smoothing factors. Too large a smoothing factor will blur the output image, which you don't want.