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Doesn't really have all with the compression though.

PNG is lossless, so it really does.

It has a compression parameter though

An image can be compressed and still lossless.

Right but it lets you adjust the level so I assumed it was lossy. But I googled it and it's not

Yeah, all kinds of lossless compression let you adjust how much CPU time is spent.

For png, you end up with a variety of settings all the way from "very weak" up to "weak".

There are none missing. (proof to the contrary for you would be easy: just list the color that is missing)