Worth checking out..
EXIF in my PENTAX dslr RAW images are as little as 3kb, not even worth considering stripping it really (if that's what you mean't??).
However, the same 9.67 MB 3036x2020 px RAW file run through PSP's optimizer at the settings suggested by Bob gives me a file 7.46 MB with EXIF and 7.43 MB without EXIF. Change the compression factor to 25% (75% quality) the file becomes 560 KB without any change to the resolution and without any noticable artifacts.
Chroma sub-sampling isn't recommended (as commented in the optimzer wizard) yet I chose 4x4 2x2 2x2 which resulted in an image size of 4.14 MB, however it failed to display in any viewer.

As asked earlier, I'd like to see the RAW file and the 700KB file which Bob created from it. I'm certain I'll find an answer if I do