It isn't always that simple.
Take the attachments to my previous post for example, neither are fuzzy and the JPG is slightly smaller at 110KB than the GIF which is 116KB. The GIF is restricted to 8-bit colour depth but apart from that it's lossless, the JPG has a colour depth of 24-bit but some detail is lost, although it's insignificant as the the quality is set to 85%.
If size is a problem, save in PNG with a reduced colour depth and maximum compression.
I've reduced to 4-bit colour depth and the file size has halved to 50.5KB but the quality hasn't suffered because the image contains less than 16 colours. If you did a similar thing to a photograph they quality would seriously suffer.
I often save schematics in 4-bit or even 1-bit colour depth PNGs because the small files size uploads quickly and I accept that some people here might be on dialup.