take my icon for example

Alright so my big issue is mainly JPEG saving. I use Photoshop to create icons and then Paint Shop to add borders. But whenever I save my icons as JPEGS, no matter whether it is a 'high' file or a 'low' file, my images turn out fuzzy. The only way sfor me to get 'clean' images without the fuzzies, I have to save it as a PNG. Is there any other way for me to clean up my JPEGS?