Tweeters don't hiss, amps and other things in the signal chain hiss and tweeters can amplify this. My guess is, that Eden is quite noisy. My Epi UL's are dead quiet with my basses and heads.
Check everything in your signal chain to see where the hiss is coming from (i.e., do you have the enhance control or treble cranked on the amp or bass, etc.).
Also, where to you have the tweeter attenuator set. I find that between 9 and 10 o'clock is the 'sweet spot' on the Epi.
Edit: While you don't have your profile filled in, so I can't know for sure, your TB name containing the word effects makes me guess you have a bunch of pedals in your signal chain. If that's true, a high quality, full range cab can amplify all the noise and crud coming through those pedals into your signal chain that you might not have noticed if you were using a cab without a tweeter previously. If this is the case, and you don't want to get rid of your effects, just turn the tweeters down.