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Could you then give me a common use where a loss not noticeable to the human eye is, in fact, important?

When saving and closing an image, only to realize you need need to change something, thus necessitating a second save, which compounds loss. Granted, if you keep a lossless file around to edit, your problem is gone. But does everyone really do that with every file?

That's the only one I could imagine encountering, and if I've not saved the original, serves me right AFAIC.

But then, if I save the second with a higher-than-otherwise-optimal setting, then I can reduce the compounding of effects. It's cost me filesize to limit loss to the imperceptible, but it's still possible.

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