Don't always blame the tweeter. That harshness is in most cases, just excessive volume, at least in good quality speakers, and not distortion/breakup.
Well, you just described compression, and this to me is a sign of a mediocre tweeter.
Room acoustics can also make systems seem harsh when you turn up the volume. The excess reverberation time in the mid-treble is more noticeable to the ear when you turn up the volume.