When I bought my '95 ZX-6R it had a 180/60-17 on the back and it was not rubbing. I replaced it with a 160/60-17 (stock size) and it handles better. I have a feeling that the 180s are on 600 mostly for looks.
i HAVE A '99 ZX6R. I just put a 180/55/17 Sportec on the back. No issues with rubbing, there's plenty of room. I have the 120/60/17 Sportec on the front and the bike handles much better. Easier turn-in, stabile at speed. Very happy with the result.
Tyres should be no trouble, BUT the rims are a dif story. I think Kawi changed the hub setup with the redesigned '00-'02. I don't know for possitive, so you might want to call a local Kawi dealer parts dept and ask them.
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