First of all, make sure the tweeter is OK. Both channels should sound the same. A damaged voice coil, or something else in the tweeter can cause this.
If you find both tweeters to sound the same, maybe your sensitive to their resonance (usually right over 20 kHz) like a lot of people are, or just the speakers design.
You can try adding a non-inductive 1-4 ohm wire wound resistor in series between the plus wire and the tweeters input plus (+) terminal. The larger the ohm number you use, will result in less output from the tweeter. Maybe try a 2 ohm to start. This will tame the tweeter down. You may, or may not like the results. I have done this myself with good results. Here is a link to give you an idea about the resistor. Link.[http://www.parts-express.com/wizards/searchResults.cfm?srchExt=CAT&srchCat=345]