Well it depends on how you mic things. If you mic the cymbals only then an aggressive HP can clear out some of the mud and leave you just the sparkle of the cymbals. If you mic'd it with say an x-y or ortf style stereo pair, then no wonder you're getting a lot of bleed.
The first thing to consider is the kit, tuning, and the mic placement. Maybe you didn't place the mics in a position where you maximize the cymbal sound and minimize what you pick up from the other drums.
That said, all these suggestions are good. Just be careful if you're limiting or side-chaining the overheads down that you aren't causing them to pump weirdly. Don't overdo it - short release times will help if you're sidechaining. If they are recorded well in a good room you probably don't need to HP at too high of a frequency, but of course that's all dependent on the cymbals, the micing, the room and whatever else is present in your mix.
Also it helps if you can post a sample and give the recording details....