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.
If the speaker has wide dispersion at high frequencies and your room is untreated or poorly treated, the total energy reaching your ear at high frequencies may be excessive, especially late arrival. Room treatment will be your friend (or a different speaker).
If the speaker has wide dispersion at high frequencies and your room is untreated or poorly treated, the total energy reaching your ear at high frequencies may be excessive, especially late arrival. Room treatment will be your friend (or a different speaker).