Compression kills detail. For challenges, always use the least amount of compression that you can and still fit your image in under the challenge limit. (As of this writing that is 150k for basic editing and 200k for advanced)
The above screenshots show the compression dialog in Photoshop Elements 7 when saving a JPG. You can set the compression level and the dialog will tell you how big the resulting file is going to be. If the "preview" box is checked, the image will reflect what the resulting image will look like at the chosen compression level.
The upper screenshot shows a high level of compression, which results in a small file size, but heavy compression artifacts are visible and there is a serious loss of detail.
In the lower sample, I have adjusted it to a compression level that fits this image into the advanced editing limit of a 200k file size. Going to a lesser compression/higher quality setting of 11 made my file exceed the challenge limit, so an amount of 10 was the best choice in this case.
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