"Fine" is fine
- RAW is more than just "much bigger space". It is the pure image as seen by the sensor in the moment of exposure. Together with some additional information (e.g. EXIF) it is stored in memory card - that's all. JPG is already processed in the camera by applying settings like Saturation, Sharpness, Contrast, Compression ... some people use Picture Styles which is nothing but a preset of all these parameters suitable for a certain image type. The result (especially of the JPG compression) is a loss of information. That's why JPG files are smaller.
As mentioned by
ericschmerick when you convert manually you have more choices for the various different parameters of the image. But if the necessary information are already crippled or lost due to JPG compression then your possibilities are limited. Better start with RAW for any conversion. Check the section "Digital Darkroom" for further details of digital workflow. Plenty of information there.