If you can cut the bitdepth to 256 colors or less, use png and/or gif. (Different argument here ;))
If you're taking screenshots of a simple webpage like this one or you have something like scans of text documents those are actually desirable in that situation. You'll get much smaller file sizes than .jpg and the edges of contrasting color like text on white background will remain nice and crisp.
You would not think anything could be bigger than a png, but these ran several megabytes each.
Both are lossless but .png uses a lossless compression.