One of the messages in the Wiki article seems to be that cropping a jpeg, except under certain specific conditions or while using special applications,
can introduce loss. It seems counterintuitive, but I think it's one of the mistakes I had been making after processing photos as psp files and converting them back to jpegs. If I understand correctly, unless you have an application specifically for loss-lessly cropping jpegs, you should go back to the editing format---psp, tif, or whatever, to do further adjustments like cropping.
But I'm easily confused, and I could be wrong.
As for the whole compression issue---I'm still working on trying to figure that one out.
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