False dichotomy. Dithering is hardly the only or even best way to reduce image sizes. Just opening his 200x200 original in my favorite editor and resaving as JPEG with my usual parameter choices reduced it from 30K to 11K with no noticeable reduction in quality. I could have tuned the parameters for even more savings.

Dithering isn't usually worth the reduction in quality. And ironically it can make things worse if you're not careful - dithering the image and saving it as JPEG actually INCREASED the size to 39K!