To much high

I definitely agree with NOT using errors in other components to fix errors in another.

Try to fix your room as much as possible. After that, add a resistor to the tweeter circuit. (This resistor must be added BEFORE the tweeter's filter cap or you'll change the crossover point. This may be easy or difficult depending on the complexity of the crossover.)
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I agree that treating the room is definitely the best approach. I will not repeat any of the excellent advice already given.

However, if that is impossible, for either room constraints or spouse constraints (Boy, I know the later!), than rather than switching speaker cables, perhaps you could try something less expensive like switching out the interconnect between your source and preamp, or between your preamp and amp.
You might want to try a Cardas Golden Cross cable. It might just take the edge off the brightness. (A friend of mine used to use these cables to take the edge off his CD player.) You should easily be able to find a used pair on Audiogon (or Ebay) and give it a shot. If it does not work, you can easily get most of your money back. (You might want to ask any friends who are audiophiles to lend you some of their cables, so you can experiment. I have lent out cables for that purpose before.)

Just a thought. Good Luck!

Definitely treat the room. And, as has been suggested, going to a different IC can often help with the shrill highs. Although I prefer silver cables with our tube-based system, I found the Audience AU24 IC and the Analysis Plus Crystal Oval both took some of the high end edge out that is present with the silver IC's. There are many excellent options out there.
Hope this helps.

Guys, thanx for the advice, I will experiment with placement and some absorbing materials. And Didactically, being an ex-radio engineer, I know how original sounds, and I know these speakers are a bit bright. But because I fell in love with their potential I'll try to squeeze out every last drop that's in them.
Jeffreybehr, if I would use a resistor to reduce tweeter output (say, 1 ohm - 5 watts), wouldn't the best place be in the '+'-cable between cross-over and tweeter? I don't know, that just seemed the most logical place, but I might be wrong here, so any advice would be appreciated. And then: is it possible to get to high? :) But you're right, I probably meant 'too much high', but since I'm from Holland I tend to mess up things like that......

Satch:
Chiming in: the room (some expense). Placement (no expense).
What lead you to silver speaker cables? Depending on implementation some silver cables can vary the highs quality... Might you have any old speakers cable to swap for a test (no expense), a friend that could lend a hand here ( you will know your next expense, if they work you don't return them one less freind though!!)?