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Peter Larsen:

I happen to operate from the gut. And my gut tells me, common sense, that the more you compress something, not only can you raise it's RMS, but the closer more of its peaks will continuously reside near full-scale.

You're absolutely right - most of the loudening effect occurs to the RMS, but the peaks become somewhat more sustained near FS too.

The crest factor - the ratio between the RMS and those peaks, diminishes.

Again, something even a child would know.